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Year 2014, Volume: 2 Issue: 1, 12 - 18, 01.04.2014
https://izlik.org/JA75SC28TN

Abstract

References

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  • J.H. He, X.H. Wu, Chaos Solitons Fractals. 30 (2006).
  • Ahmet Bekir, Comm. Nonlinear Sci. Numer. Simulat. 13, 9 (2008).
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  • 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
https://izlik.org/JA75SC28TN

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

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

Authors

Ahmet Bekir This is me

Abdelfattah El Achab This is me

Publication Date April 1, 2014
IZ https://izlik.org/JA75SC28TN
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. https://izlik.org/JA75SC28TN
AMA 1.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):12-18. https://izlik.org/JA75SC28TN
Chicago Bekir, Ahmet, and Abdelfattah El Achab. 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. https://izlik.org/JA75SC28TN.
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 [1]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, Apr. 2014, [Online]. Available: https://izlik.org/JA75SC28TN
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 1, 2014): 12-18. https://izlik.org/JA75SC28TN.
JAMA 1.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, Apr. 2014, pp. 12-18, https://izlik.org/JA75SC28TN.
Vancouver 1.Ahmet Bekir, 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 [Internet]. 2014 Apr. 1;2(1):12-8. Available from: https://izlik.org/JA75SC28TN