International Journal of Mathematical Research

Published by: Conscientia Beam
Online ISSN: 2306-2223
Print ISSN: 2311-7427
Quick Submission    Login/Submit/Track

No. 1

The (F/G)-Expansion Method and Travelling Wave Solutions of Nonlinear Evolution Equations

Pages: 63-74
Find References

Finding References


The (F/G)-Expansion Method and Travelling Wave Solutions of Nonlinear Evolution Equations

Search :
Google Scholor
Search :
Microsoft Academic Search
Cite

DOI: 10.18488/journal.24/2016.5.1/24.1.63.74

Ä°brahim Celik

Export to    BibTeX   |   EndNote   |   RIS

Untitled Document
  1. M. J. Ablowitz and P. A. Clarkson, Solitons, nonlinear evolution equations and inverse scattering transform. Cambridge: Cambridge Univ. Press, 1991.
  2. C. Rogers and W. F. Shadwick, Backlund transformations. New York: Academic Press, 1982.
  3. M. Wadati, H. Sanuki, and K. Konno, "Relationships among inverse method, bäcklund transformation and an infinite number of conservation laws," Prog. Theor. Phys., vol. 53, pp. 419-436, 1975.
  4. V. A. Matveev and M. A. Salle, Darboux transformation and solitons. Berlin: Springer, 1991.
  5. R. Hirota, "Exact envelope soliton solutions of a nonlinear wave equation," J. Math. Phys., vol. 14, pp. 805-810, 1973.
  6. F. Cariello and M. Tabor, "Similarity reduction from extended Painlevé expansion for nonintegrable evolution equations," Physica D, vol. 53, pp. 59-70, 1991.
  7. E. J. Parkes and B. R. Duffy, "An automated tanh-function method for finding solitary wave solutions to nonlinear evolution equations," Comput. Phys. Commun., vol. 98, pp. 288-300, 1996.
  8. E. G. Fan, "Extended tanh-function method and its applications to nonlinear equations," Phys. Lett. A., vol. 277, pp. 212-218, 2000.
  9. Z. Y. Yan, "New explicit travelling wave solutions for two new integrable coupled nonlinear evolution equations," Phys. Lett. A., vol. 292, pp. 100-106, 2001.
  10. S. K. Liu, Z. T. Fu, S. D. Liu, and Q. Zhao, "Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations," Phys. Lett. A., vol. 289, pp. 69-74, 2001.
  11. Z. Y. Yan, "Abundant families of Jacobi elliptic functions of the (2 + 1)-dimensional integrable Davey-Stewartson-type equation via a new method," Chaos Solitons Fractals, vol. 18, pp. 299-30, 2003.
  12. M. L. Wang and Y. B. Zhou, "The periodic wave equations for the Klein-Gordon-Schordinger equations," Phys. Lett. A., vol. 318, pp. 84-92, 2003.
  13. Y. B. Zhou, M. L. Wang, and T. D. Miao, "The periodic wave solutions and solitary wave solutions for a class of nonlinear partial differential equations," Phys. Lett. A., vol. 323, pp. 77- 88, 2004.
  14. M. L. Wang and X. Z. Li, "Extended F-expansion and periodic wave solutions for the generalized Zakharov equations," Phys. Lett. A., vol. 343, pp. 48-54, 2005.
  15. M. L. Wang and X. Z. Li, "Applications of F-expansion to periodic wave solutions for a new hamiltonian amplitude equation," Chaos, Solitons and Fractals, vol. 24 pp. 1257-1268, 2005.
  16. J. L. Zhang, M. L. Wang, and X. Z. Li, "The subsidiary ordinary differential equations and the exact solutions of the higher order dispersive nonlinear Schrödinger equation," Phys. Lett. A., vol. 357, pp. 188-195, 2006.
  17. M. L. Wang, X. Z. Li, and J. L. Zhang, "Various exact solutions of nonlinear Schrödinger equation with two nonlinear terms," Chaos Solitons Fractals, vol. 31, pp. 594-601, 2007.
  18. X. Z. Li and M. L. Wang, "A sub-ODE method for finding exact solutions of a generalized KdV–mKdV equation with high-order nonlinear terms," Phys. Lett. A., vol. 361, pp. 115- 118, 2007.
  19. M. L. Wang, X. Z. Li, and J. L. Zhang, "Sub-ODE method and solitary wave solutions for higher order nonlinear Schrödinger equation," Phys. Lett. A., vol. 363, pp. 96-101, 2007.
  20. M. L. Wang, "Solitary wave solutions for variant Boussinesq equations," Phys. Lett. A., vol. 199, pp. 169-172, 1995.
  21. M. L. Wang, "Exact solutions for a compound KdV-burgers equation," Phys. Lett. A., vol. 213, pp. 279-287, 1996.
  22. M. L. Wang, Y. B. Zhou, and Z. B. Li, "Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics," Phys. Lett. A., vol. 216, pp. 67-75, 1996.
  23. A. M. Wazwaz, "Distinct variants of the KdV equation with compact and noncompact structures," Appl. Math. Comput., vol. 150, pp. 365-377, 2004.
  24. A. M. Wazwaz, "Variants of the generalized KdV equation with compact and noncompact structures," Comput. Math. Appl., vol. 47, pp. 583-591, 2004.
  25. X. Feng, "Exploratory approach to explicit solution of nonlinear evolutions equations," Int. J. Theo. Phys., vol. 39, pp. 207-222, 2000.
  26. J. L. Hu, "A new method for finding exact traveling wave solutions to nonlinear partial differential equations," Phys. Lett. A., vol. 286, pp. 175-179, 2001.
  27. J. L. Hu, "Explicit solutions to three nonlinear physical models," Phys. Lett. A., vol. 287, pp. 81-89, 2001.
  28. J. L. Hu, "A new method of exact traveling wave solution for coupled nonlinear differential equations," Phys. Lett. A., vol. 322, pp. 211-216, 2004.
  29. J. H. He and X. H. Wu, "Exp-function method for nonlinear wave equations," Chaos, Solitons and Fractals, vol. 30, pp. 700-708, 2006.
  30. M. Wang, X. Li, and J. Zhang, "The  -expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics," Phys. Lett. A., vol. 372, pp. 417–423, 2008.
  31. M. Wang, X. Li, and J. Zhang, "Application of  -expansion method to travelling wave solutions of the broer-kaup and the approximate long water wave equations," Appl. Math. Comput., vol. 206, pp. 321–326, 2008.
  32. A. Ismail, "Exact and explicit solutions to some nonlinear evolution equations by utilizing the  -expansion method," Appl. Math. Comput., vol. 215, pp. 857-863, 2009.
  33. J. Zhang, X. Wei, and Y. Lu, "A generalized - expansion method and its applications," Phys. Lett. A., vol. 372, pp. 3653–3658, 2008.
  34. S. Zhang, W. Wang, and J. L. Tong, "A generalized  -expansion method and its application to the (2+1)-dimensional broer-kaup equations," Appl. Math. Comput., vol. 209, pp. 399–404, 2009.
  35. S. Zhang, J. L. Tong, and W. Wang, "A generalized  -expansion method for the mKdV equation with variable coefficients," Phys. Lett. A., vol. 372, pp. 2254–2257, 2008.
  36. S. Zhong, L. Dong, J. Ba, and Y. Sun, "The  -expansion method for nonlinear differential-difference equations," Phys. Lett. A., vol. 373, pp. 905–910, 2009.
  37. Z. Yu-Bin and L. Chao, "Application of modified  -expansion method to traveling wave solutions for Whitham broer kaup-like equations," Commu. Theor. Phys., vol. 51, pp. 664–670, 2009.
  38. G. B. Whitham, Linear and nonlinear waves. New York: Academic Press, 1973.
  39. Z. T. Fu, S. D. Liu, and S. K. Liu, "New solutions to mKdV equation," Phys. Lett. A., vol. 326, pp. 364-374, 2004.
  40. V. V. Gudkov, "A family of exact travelling wave solutions to nonlinear evolution and wave equations," J. Math. Phys., vol. 38, pp. 4794-4803, 1997.
  41. W. X. Ma and B. Fuchssteiner, "Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation," Int. J. Nonlinear Mech., vol. 31, pp. 329-338, 1996.
  42. M. Yoshimasa, "Reduction of dispersionless coupled Korteweg–De Vries equations to the Euler–Darboux equation," J. Math. Phys., vol. 42, pp. 1744-1760, 2001.
Ä°brahim Celik (2016). The (F/G)-Expansion Method and Travelling Wave Solutions of Nonlinear Evolution Equations. International Journal of Mathematical Research, 5(1): 63-74. DOI: 10.18488/journal.24/2016.5.1/24.1.63.74
The (F/G)-expansion method is firstly proposed, where F=F(ξ) and  G = G(ξ) satisfies a first order ordinary differential equation systems (ODEs). We give the exact travelling wave solutions of the variant Boussinesq equations and the KdV equation and by using (F/G)-expansion method. When some parameters of present method are taken as special values, results of the  -expansion method are also derived. Hence,  -expansion method is sub method of the proposed method. The travelling wave solutions are expressed by three types of functions, which are called the trigonometric functions, the rational functions, and the hyperbolic functions. The present method is direct, short, elementary and effective, and is used for many other nonlinear evolution equations.

Contribution/ Originality
This study contributes in the existing literature of  -expansion method. We proposed the (F/G)-expansion method and investigated the exact travelling wave solutions of the variant Boussinesq equations and the KdV equation by using (F/G)-expansion method.

Properties of Permutation Groups Using Wreath Product

Pages: 58-62
Find References

Finding References


Properties of Permutation Groups Using Wreath Product

Search :
Google Scholor
Search :
Microsoft Academic Search
Cite

DOI: 10.18488/journal.24/2016.5.1/24.1.58.62

Achaku, David Terna , Abam, Ayeni Omini

Export to    BibTeX   |   EndNote   |   RIS

  1. M. A. Arbib, Algebraic theory of machines, languages and Semi-groups. New York: Academic Press, 1968.
  2. R. P. Hunter, "Some results on wreath products of Semi-groups," Bull Soc. Math. Belgique, vol. 18, pp. 3-16, 1966.
  3. Y. G. Kosheler, "Wreath products and equations in Semi-groups," Semi-Groups Forum, vol. 11, pp. 1-13, 1975.
  4. S. Nakajima, "On the Kernel of the wreath product of completely simple Semi-groups 11," presented at the First Symp., 1977.
  5. K. Krohn and J. Rhodes, "Algebraic theory of machines. Prime decomposition theorem for finite semi- groups and machines," Trans. American Math. Soc., vol. 116, pp. 450-464, 1965.
Achaku, David Terna , Abam, Ayeni Omini (2016). Properties of Permutation Groups Using Wreath Product. International Journal of Mathematical Research, 5(1): 58-62. DOI: 10.18488/journal.24/2016.5.1/24.1.58.62
Classification of the p-subgroups of the finite group of order 12 was done using Cauchy’s Lagrange’s and Sylow’s Theorems up to Isomorphism subgroups and related to the Dihedral group of order 20 (D2n) in Chemical Bonding.

Contribution/ Originality

MHD Mixed Convective Heat and Mass Transfer through a Stratified Nanofluid Flow Over a Thermal Radiative Stretching Cylinder

Pages: 40-57
Find References

Finding References


MHD Mixed Convective Heat and Mass Transfer through a Stratified Nanofluid Flow Over a Thermal Radiative Stretching Cylinder

Search :
Google Scholor
Search :
Microsoft Academic Search
Cite

DOI: 10.18488/journal.24/2016.5.1/24.1.40.57

Srinivas Maripala , Kishan Naikoti

Export to    BibTeX   |   EndNote   |   RIS

  1. S. U. S. Choi, "Enhancing thermal conductivity of fluids with nanoparticles," presented at the The Proceedings of the ASME International Mechanical Engineering Congress and Exposition, ASME, FED 231/MD, USA, 1995.
  2. S. Ozernic, S. Kakac, and A. G. Yazicioglu, "Enhanced thermal conductivity ofnano fluids: A state of the art review," Microfluid. Nanofluid, vol. 8, pp. 145–170, 2012.
  3. R. Kandasamy, P. Loganathan, and P. P. Arasu, "Scaling group transformation for MHD boundary layer flow of a nanofluid past a vertical stretching surface in thepresence of suction and injection," Nuclear Eng. Design, vol. 241, pp. 2053–2059, 2011.
  4. C. R. Lin and Y. P. Shih, "Laminar boundary layer heat transfer alongstatic and moving cylinder," J. Chin. Inst. Eng., vol. 3, pp. 73 –79, 1980.
  5. C. R. Lin and Y. P. Shih, "Buoyancy effects on the laminar boundarylayer heat transfer along vertically moving cylinder," J. Chin. Inst. Eng., vol. 4, pp. 45 – 51, 1981.
  6. C. Y. Wang, "Fluid flow due to a stretching cylinder," Phys. Fluids, vol. 31, pp. 466–468, 1988.
  7. A. Ishak, R. Nazar, and I. Pop, "Magnetohydrodynamic (MHD) flow andheat transfer due to a stretching cylinder," Energy Convers Manag., vol. 49, pp. 3265 – 3269, 2008.
  8. E. M. A. Elbashbeshy, T. G. Emam, M. S. El – Azab, and K. M. Abdelgaber, "Laminarboundary layer flow along a stretching horizontal cylinderembedded in a porous medium in the presence of a heat source or sinkwith suction/injection," International Journal of Energy & Technology, vol. 4, pp. 1 – 6, 2012.
  9. R. Nazar, L. Tham, I. Pop, and D. Ingham, "Mixed convection boundary layer flow from a horizontalcircular cylinder embedded in a porous medium filled with a nanofluid," Transport in Porous Media, vol. 86, pp. 517–536, 2011.
  10. R. Saidur, K. Leong, and H. Mohammad, "A review on applications and challenges of nanofluids," Renewable and Sustainable Energy Reviews, vol. 15, pp. 1646-1668, 2011.
  11. X. Q. Wang and A. S. Mujumdar, "Heat transfer characteristics of nanofluids: A review," International Journal of Thermal Sciences, vol. 46, pp. 1–19, 2007.
  12. P. Cheng, "Mixed convection about a horizontal cylinder and sphere in a fluid-saturated porousmedium," International Journal of Heat and Mass Transfer, vol. 25, pp. 1245–1246, 1982.
  13. D. A. Nield and A. Bejan, Convection in porous media. New York, USA: Springer, 2013.
  14. K. Khanafer and K. Vafai, "A critical synthesis of thermophysical characteristics of nanofluids," International Journal of Heat and Mass Transfer, vol. 54, pp. 4410–4428, 2011.
  15. M. Srinivas and N. Kishan, "Unsteady MHD flow and heat transfer of nanofluid over a permeable shrinking sheet with thermal radiation and chemical reaction," American Journal of Engineering Research, vol. 4, pp. 68-79, n.d.
  16. M. Macha and N. Kishan, "Magnetohydrodynamic mixed convection stagination-point flow of a power-law non-newtonian nanofluid towards a stretching surface with radiation and heat source/sink," Journal of Fluids, Hindawi Publishing Corporation, vol. 2015, pp. 1-14, 2015.
  17. T. Poornima and R. N. Bhaskar, "Mixed convection heat and mass transfer flow along a stretching cylinder in a thermally stratified medium with thermal radiation effects," Journal of Global Research in Mathematical Archives, vol. 1, pp. 72-82, 2015.
  18. M. Q. Brewster, Thermal radiative transfer properties. New York, USA: Wiley, 1992.
Srinivas Maripala , Kishan Naikoti (2016). MHD Mixed Convective Heat and Mass Transfer through a Stratified Nanofluid Flow Over a Thermal Radiative Stretching Cylinder. International Journal of Mathematical Research, 5(1): 40-57. DOI: 10.18488/journal.24/2016.5.1/24.1.40.57
The flow problem presented in this paper is to study the heat and mass transfer characteristics of a mixed convection nanofluid flow along a stretching cylinder embedded in a thermally stratified medium are numerically analyzed, with the thermal radiation effects. The governing boundary layer equations of continuity, momentum, energy and concentration are transformed into a set of ordinary differential equations with the help of suitable local similarity transformations. The coupled non-linear ordinary differential equations are solved by the implicit finite difference method along with the Thomas algorithm. The effect of various material parameters such as buoyancy parameter, solutal buoyancy parameter, Prandtl number, radiation parameter, Schmidt number, curvature parameter, magnetic parameter, stratification parameter, Brownian motion parameter and thermophoresis parameter on the velocity, temperature and concentration profiles are presented in graphs. Physical quantities such as skin friction coefficient, Nusselet number and Sherwood number are also computed. 

Contribution/ Originality
The primary contribution of this paper is finding that the effects of nanofluid on the heat and mass transfer characteristics of a mixed convection along a radiative stretching cylinder embedded in a thermal stratified medium. Aim of this paper is to develop a computational procedure.

Riccatis Equation. Asymptotics of Exact Solution

Pages: 25-39
Find References

Finding References


Riccatis Equation. Asymptotics of Exact Solution

Search :
Google Scholor
Search :
Microsoft Academic Search
Cite

DOI: 10.18488/journal.24/2016.5.1/24.1.25.39

Nikolai Evgenievich Tsapenko

Export to    BibTeX   |   EndNote   |   RIS

  1. E. F. Kuester, "A lower bound for the length of nonuniform transmission line matching sections," Int. J. Electron. Commun. AEÜ, vol. 66, pp. 1011- 1016, 2012.
  2. N. E. Tsapenko, "Plane electromagnetic waves in heterogeneous medium approximation regarding relative rate of change of wave resistance," Laser and Particle Beams, vol. 11, pp. 679-684, 1993.
  3. S. K. Younis and N. E. Tsapenko, "New solution method of wave problems from the turning points," International Journal of Energy and Power Engineering. Science Publishing Group, USA, vol. 3, pp. 15-20, 2014.
  4. N. E. Tsapenko, "New formulas for an approximate solution of the one-dimensional wave equation," Differential Equations, vol. 25, pp. 1941-1946, 1989.
  5. N. E. Tsapenko, Riccatis's equation and wave processes. Moscow: MSMU-Publisher, Gornaya Kniga, 2008.
Nikolai Evgenievich Tsapenko (2016). Riccatis Equation. Asymptotics of Exact Solution. International Journal of Mathematical Research, 5(1): 25-39. DOI: 10.18488/journal.24/2016.5.1/24.1.25.39
In this article based on a method of approximating equation an asymptotic solution of the general Riccati ‘s equation is obtained. The principal distinctive feature and advantage of the solution is its continuity at turning points. Estimates of accuracy of the approximate solution are derived. Limit values of the asymptotic solution in case of one-sided convergence of argument to turning point of the first order are calculated.

Contribution/ Originality
This study contributes in the existing literature. Thus, the results of that study may be applied for solving problems were set up in works [1], [2], [3]. This study is one of very few studies, which have investigated the asymptotic behavior of solutions of Riccati’s equation in the neighborhood of turning points.

Mathematical & Spatial Relationship between Dome and Al- Mousala in Congregational Mosques (An Analytical Study of Basic Dimension of Central Dome Pattern)

Pages: 1-24
Find References

Finding References


Mathematical & Spatial Relationship between Dome and Al- Mousala in Congregational Mosques (An Analytical Study of Basic Dimension of Central Dome Pattern)

Search :
Google Scholor
Search :
Microsoft Academic Search
Cite

DOI: 10.18488/journal.24/2016.5.1/24.1.1.24

Raeed Salim Ahmed Al-Nuamman

Export to    BibTeX   |   EndNote   |   RIS

  1. Abedal- Fattah and K. Ahmed. (1988) The mosque review of historical and modern models of mosques in the muslim world. Architectural Magazine, GS. 63.
  2. Al- Hadethe, C. Abdul, and H. A. K. Atta Sabri, Conical domes in Iraq. Baghdad: The Directorate of Antiquities, The Freedom House Printing, 1979.
  3. A. F. Fikri, Mosque in Kairouan. Egypt: Knowledge House, 1965.
  4. A. D. I. N. Abbou, "Stringed domes in Mosul." Encyclopedia of Mosul cultural, Iraq, mousl / c 3, 1992.
  5. A. R. Ghazi, Islamic art and function of islamic architecture the shape response, c 1. Egypt: Knowledge House, 1984.
  6. M. S. Lamaee, Domes in islamic architecture. Beirut: Arab Renaissance Publishing House Printing and Publishing, 1987.
  7. D. Maher and M. Saad, Evolution of the dome in islamic architecture. Cairo: The Supreme Council for Islamic Affairs, 1988.
  8. Ouaili and A.-D. Keer, The mosque in islam rulings and etiquette and heresy. Damascus: Islamic Library, 1414.
  9. I. I. Shahata, Cairo. Cairo: General Book Organization, 1999.
  10. S. Sabic, Fekh al-suna, m 1, m 10. Cairo: Arab Conquest Media, 1993.
  11. M. N. Hassan, "The characteristics of thinking in the design of the internal space of the mosque, research published," presented at the Symposium Mosque Architecture, College of Architecture and Planning, King Saud University, Riyadh, 1999.
  12. AL- Mamouri and S. S. A.-M. Abdullah, "Humanitarian Arab islamic architecture," Iraqi Journal of Architecture, University of Technology, Section Architect, vol. 7, 2010.
  13. O. Grabber, The formation of islamic art. New Havened London: Yale University Press, 1973.
  14. Al-Umari and R. Hafsa, "The impact of islamic religion in the formation of buildings urbanism," University of Baghdad, Unpublished PhD Thesis, 2000.
  15. Al- Jubouri and M. Samaan, "Geometric characteristics in Islamic architecture," Master Unpublished, The University of Technology, Baghdad, 1998.
  16. N. Ardalan and B. Laleh, The sense of unity and Sufi tradition in person architecture. Chicago: University of Chicago, Press, 1980.
  17. Al-Maliki and F. Kbila, Geometric and mathematics in the Arab-Islamic architecture, study of proportionality, organizations and systems of proportionality. Amman: Al-Safa House for Publishing and Distribution, 2002.
  18. G. Michel, Architecture of the islamic world, 1ts history and social meaning. New York: Tom and Hudson, 1978.
  19. H. R. Al-Umari, "The architecture of modern mosques in Iraq," Baghdad University, Msc Thesis, 1988.
  20. Hillenbr and Robert, Islamic architecture form, function, meaning. Edinburgh: Edinburgh University Press 1994.
  21. R. Mantran, History of the Ottoman state, 1st ed. Cairo: Bashir Translation Sevenfold Part II House Thought of Studies, Publication and Distribution, 1993.
  22. A. Y. T. Taieb, "Architectural conservation in mosques," Sulimania Journal, practical experience in Alrabaah mosque in Mosul documenting, 2001.
No any video found for this article.
Raeed Salim Ahmed Al-Nuamman (2016). Mathematical & Spatial Relationship between Dome and Al- Mousala in Congregational Mosques (An Analytical Study of Basic Dimension of Central Dome Pattern). International Journal of Mathematical Research, 5(1): 1-24. DOI: 10.18488/journal.24/2016.5.1/24.1.1.24
Islamic architecture has a clear impact for systems and the relationships of Mathematical and  Geometrical proportions , which reflected in their buildings.  The research will deal with an important aspect that linked in two mains elements in the Congregational Mosques. The first is a house of prayer (Al-mousala) as the main and most importantly space in the mosque, and the second is a dome as structural and decorative element, who was significantly associated with Congregational Mosques later. This study is one of very few studies which have investigated the kind of the Mathematical& Geometrical proportions relationship, also the  spatial linking of these two elements with each other's.  Through the statistical analysis that links the relationship between their different dimensions and the positioning kind of the main dome on a house of prayer (Al-mousala). For this purpose the resaerch has been selected two sets of samples. The first models include a different regions of Islamic Congregational Mosques represent different patterns of Congregational Mosques as a sample of general Islamic architecture while the second comprises a number of Congregational Mosques in Mosul city, a representative of the local architecture.



Contribution/ Originality