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Year 2014, Volume: 2 Issue: 1, 12 - 18, 01.04.2014

Ahmet Bekir Abdelfattah El Achab

Abstract

References

  • P. Rosenau, J. M. Hyman, Phys.Rev. Lett. 70 (5) (1993).
  • J. H. He, Int. J Nonlinear Sci. Numer. Simulat. 6 (2) (2005).
  • J. H. He, X. H. Wu, Chaos, Solitons and Fractals 30 (3) (2006).
  • J. H. He, X. H.Wu, Chaos, Solitons and Fractals 29 (1) (2006).
  • J. H. He Int. J Modern Phys. B 20 (10) (2006).
  • L. Xu,Chaos, Solitons and Fractals 37 (1) (2008).
  • A. M. Wazwaz, Math. Comput. Simulat. 59 (6) (2002).
  • A. M. Wazwaz, Appl. Math. Comput. 132 (1) (2002).
  • Y. Chen, B. Li, H. Q. Zhang, Math. Comput. Simul. 64 (5) (2004).
  • B. He, Q. Meng, W. Rui , Y. Long, Commun. Nonlinear Sci. Numer.Simulat. 13 (2008).
  • Z. Y. Yan, Comput. Phys. Commun. 152 (1) (2003).
  • Z. Y. Yan, Comput. Phys. Commun. 153 (1) (2003).
  • A. Biswas, Phys. Lett. A 372 (25) (2008).
  • Y. G. Zhu, K. Tong, T. C. Lu, Chaos, Solitons and Fractals 33 (4) (2007).
  • C. H. Xu, L. X. Tian, Chaos, Solitons and Fractals 40 (2) (2009).
  • T. C. Xia, Appl. Math. E-Notes 3(2003).
  • D. Lu, B. Hong, L. Tian, International Journal of Nonlinear Science 2(2OO6). M.R. Miura, B¨aacklund Transformation, Springer, Berlin, 1978.
  • R. Hirota, The direct method in soliton theory, Cambridge UniversityPress, Cambridge, 2004.
  • W. Mal.iet, Am. J. Phys. 60, 7(1992).
  • A. M. Wazwaz, Appl. Math. Comput. 138 (2/3) (2003).
  • E. Fan, Phys. Lett. A. 277 (2000).
  • Ahmet Bekir, International Journal of Nonlinear Sciences and Numerical Simulation, 10, (6) 735-739. X. D. Zheng, T. C. Xia and H. Q. Zhang, Appl. Math. E-Notes 2 (2002).
  • A.M.Wazwaz, Math. and Comput. Modelling. 15 (1982).
  • F. Tascan, Ahmet Bekir,Applied Mathematics and Computation, 215 (8) (2009).
  • M. Inc, M. Ergut, Appl Math E-Notes 5 (2005).
  • H.-T. Chen, H.-Q. Zhang, Chaos Solitons Fractals 20 (2004).
  • Z. S. Feng, Phys. Lett. A. 293(2002).
  • F. Tascan, Ahmet Bekir, M. Koparan, Comm. Nonlinear Sci. Numer.Simulat. 14 (5) 1810-1815.
  • Ahmet Bekir, O. Unsal, Physica Scripta, 85 065003 (2012)
  • G. Ebadi and A. Biswas, Comm. Nonlinear Sci. Numer. Simulat. 16,2377 (2011).
  • R. S. Banerjee, Phs. Scr. 57(5), 598 (1998).
  • T.R. Ding, C.Z. Li, Ordinary Differential Equations, Peking University Press, Peking, 1996.
  • N. Bourbaki, Commutative Algebra, Addison Wesley, Paris, 1972.
  • J.H. He, X.H. Wu, Chaos Solitons Fractals. 30 (2006).
  • Ahmet Bekir, Comm. Nonlinear Sci. Numer. Simulat. 13, 9 (2008).
  • M.S. Bruz´on, M.L. Gandarias, Mathematical Methods in the Applied Science 2010, DOI: 10.1002/mma.1339.
  • M.S. Bruz´on, M.L. Gandarias, G.A. Gonz´alez, R. Hansen, Applied Mathematics and Computation vol. 218, issue 20, 2012.
  • M. J. Ablowitz and H. Segur, Solitons and inverse scattering transform, Philadelphia, SIAM, 1981.
  • B. P. Palka, An Introduction to Complex Function Theory, Spring-Verlag, New York, 1991.

Traveling Wave Solutions to the K(m,n) equation with generalized evolution Using the First Integral Method

Year 2014, Volume: 2 Issue: 1, 12 - 18, 01.04.2014

Ahmet Bekir Abdelfattah El Achab

Abstract

In this paper, we investigate the first integral method for solving the K (m, n) equation with generalized evolution.(un)+ a(um)ux + b(un)xxx = 0 t A class of traveling wave solutions for the considered equations are obtained where 4n = 3(m + 1). This idea can obtain some exactsolutions of this equations based on the theory of Commutative algebra

Keywords

Traveling wave solutions First integral method K (m n) equation

References

  • P. Rosenau, J. M. Hyman, Phys.Rev. Lett. 70 (5) (1993).
  • J. H. He, Int. J Nonlinear Sci. Numer. Simulat. 6 (2) (2005).
  • J. H. He, X. H. Wu, Chaos, Solitons and Fractals 30 (3) (2006).
  • J. H. He, X. H.Wu, Chaos, Solitons and Fractals 29 (1) (2006).
  • J. H. He Int. J Modern Phys. B 20 (10) (2006).
  • L. Xu,Chaos, Solitons and Fractals 37 (1) (2008).
  • A. M. Wazwaz, Math. Comput. Simulat. 59 (6) (2002).
  • A. M. Wazwaz, Appl. Math. Comput. 132 (1) (2002).
  • Y. Chen, B. Li, H. Q. Zhang, Math. Comput. Simul. 64 (5) (2004).
  • B. He, Q. Meng, W. Rui , Y. Long, Commun. Nonlinear Sci. Numer.Simulat. 13 (2008).
  • Z. Y. Yan, Comput. Phys. Commun. 152 (1) (2003).
  • Z. Y. Yan, Comput. Phys. Commun. 153 (1) (2003).
  • A. Biswas, Phys. Lett. A 372 (25) (2008).
  • Y. G. Zhu, K. Tong, T. C. Lu, Chaos, Solitons and Fractals 33 (4) (2007).
  • C. H. Xu, L. X. Tian, Chaos, Solitons and Fractals 40 (2) (2009).
  • T. C. Xia, Appl. Math. E-Notes 3(2003).
  • D. Lu, B. Hong, L. Tian, International Journal of Nonlinear Science 2(2OO6). M.R. Miura, B¨aacklund Transformation, Springer, Berlin, 1978.
  • R. Hirota, The direct method in soliton theory, Cambridge UniversityPress, Cambridge, 2004.
  • W. Mal.iet, Am. J. Phys. 60, 7(1992).
  • A. M. Wazwaz, Appl. Math. Comput. 138 (2/3) (2003).
  • E. Fan, Phys. Lett. A. 277 (2000).
  • Ahmet Bekir, International Journal of Nonlinear Sciences and Numerical Simulation, 10, (6) 735-739. X. D. Zheng, T. C. Xia and H. Q. Zhang, Appl. Math. E-Notes 2 (2002).
  • A.M.Wazwaz, Math. and Comput. Modelling. 15 (1982).
  • F. Tascan, Ahmet Bekir,Applied Mathematics and Computation, 215 (8) (2009).
  • M. Inc, M. Ergut, Appl Math E-Notes 5 (2005).
  • H.-T. Chen, H.-Q. Zhang, Chaos Solitons Fractals 20 (2004).
  • Z. S. Feng, Phys. Lett. A. 293(2002).
  • F. Tascan, Ahmet Bekir, M. Koparan, Comm. Nonlinear Sci. Numer.Simulat. 14 (5) 1810-1815.
  • Ahmet Bekir, O. Unsal, Physica Scripta, 85 065003 (2012)
  • G. Ebadi and A. Biswas, Comm. Nonlinear Sci. Numer. Simulat. 16,2377 (2011).
  • R. S. Banerjee, Phs. Scr. 57(5), 598 (1998).
  • T.R. Ding, C.Z. Li, Ordinary Differential Equations, Peking University Press, Peking, 1996.
  • N. Bourbaki, Commutative Algebra, Addison Wesley, Paris, 1972.
  • J.H. He, X.H. Wu, Chaos Solitons Fractals. 30 (2006).
  • Ahmet Bekir, Comm. Nonlinear Sci. Numer. Simulat. 13, 9 (2008).
  • M.S. Bruz´on, M.L. Gandarias, Mathematical Methods in the Applied Science 2010, DOI: 10.1002/mma.1339.
  • M.S. Bruz´on, M.L. Gandarias, G.A. Gonz´alez, R. Hansen, Applied Mathematics and Computation vol. 218, issue 20, 2012.
  • M. J. Ablowitz and H. Segur, Solitons and inverse scattering transform, Philadelphia, SIAM, 1981.
  • B. P. Palka, An Introduction to Complex Function Theory, Spring-Verlag, New York, 1991.
There are 39 citations in total.

Details

Journal Section Articles
Authors

Ahmet Bekir This is me

Abdelfattah El Achab This is me

Publication Date April 1, 2014
Published in Issue Year 2014 Volume: 2 Issue: 1

Cite

APA Bekir, A., & Achab, A. E. (2014). Traveling Wave Solutions to the K(m,n) equation with generalized evolution Using the First Integral Method. New Trends in Mathematical Sciences, 2(1), 12-18.
AMA Bekir A, Achab AE. Traveling Wave Solutions to the K(m,n) equation with generalized evolution Using the First Integral Method. New Trends in Mathematical Sciences. April 2014;2(1):12-18.
Chicago Bekir, Ahmet, and Abdelfattah El Achab. “Traveling Wave Solutions to the K(m,n) Equation With Generalized Evolution Using the First Integral Method”. New Trends in Mathematical Sciences 2, no. 1 (April 2014): 12-18.
EndNote Bekir A, Achab AE (April 1, 2014) Traveling Wave Solutions to the K(m,n) equation with generalized evolution Using the First Integral Method. New Trends in Mathematical Sciences 2 1 12–18.
IEEE A. Bekir and A. E. Achab, “Traveling Wave Solutions to the K(m,n) equation with generalized evolution Using the First Integral Method”, New Trends in Mathematical Sciences, vol. 2, no. 1, pp. 12–18, 2014.
ISNAD Bekir, Ahmet - Achab, Abdelfattah El. “Traveling Wave Solutions to the K(m,n) Equation With Generalized Evolution Using the First Integral Method”. New Trends in Mathematical Sciences 2/1 (April 2014), 12-18.
JAMA Bekir A, Achab AE. Traveling Wave Solutions to the K(m,n) equation with generalized evolution Using the First Integral Method. New Trends in Mathematical Sciences. 2014;2:12–18.
MLA Bekir, Ahmet and Abdelfattah El Achab. “Traveling Wave Solutions to the K(m,n) Equation With Generalized Evolution Using the First Integral Method”. New Trends in Mathematical Sciences, vol. 2, no. 1, 2014, pp. 12-18.
Vancouver Bekir A, Achab AE. Traveling Wave Solutions to the K(m,n) equation with generalized evolution Using the First Integral Method. New Trends in Mathematical Sciences. 2014;2(1):12-8.