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THE EXACT TRAVELING WAVE SOLUTIONS TO ONE INTEGRABLE KDV6 EQUATION

Year 2013, Volume 3, Issue 2, 0 - 8, 01.12.2013

Abstract

The traveling wave system of one integrable KdV6 equation is studied by using Cosgrove’s method. Some exact explicit traveling wave solutions are obtained. The local dynamical behavior of some known equilibria are discussed.

References

  • [1] A. Karasu-Kalkanli, A. Karasu, A. Sakovich, et al., A New Integrable Generalization Of The Korteweg-de Vries Equation , J. Math. Phys., 49(2008)073516-073525.
  • [2] B. A. Kupershmidt, KdV6: An Integrable System, Phys. Lett. A 372(2008)2634–2639.
  • [3] B. A. Kupershmidt, A Super KdV Equation: An Integrable System, Phys. Lett. A 102(1984)213–215.
  • [4] Y. Q. Yao, Y. B. Zeng, The Bi-Hamiltonian Structure And New Solutions Of KdV6 Equation , Lett. Math. Phys., 86(2008)193-208.
  • [5] A. Ramani, B. Grammaticos, R. Willox, Bilinearize And Solutions Of The KdV6 , Anal. Appl., 6(2008)401-412.
  • [6] R. Hirota, Direct Methods In Soliton Theory, Springer, Berlin, 1980.
  • [7] A. M. Wazwaz, The Integrable KdV6 Equations: Multiple Soliton Solutions And Multiple Singular Soliton Solutions , Appl. Math. Comput. 204(2008)963–972.
  • [8] C. A. G´omez, A. Salas, The Cole-Hopf Transformation And Improved Tanh-coth Method Applied To New Integrable System (KdV6) , Appl. Math. Comput. 204(2008)957–962.
  • [9] J. B. Li, Y. Zhang, The Exact Traveling Wave Solutions To Two Integrable KdV6 Equations , Chin. Ann. Math. 33B(2)(2012)179–190.
  • [10] D. Kaup, On The Inverse Scattrin Problem For The Cubic Eigenvalue Problems Of The Class Ψ3x + 6QΨx + 6RΨ = λΨ, Stud. Appl. Math. 62(1980)189–216.
  • [11] M. C. Cosgrove, Higher-order Painleve Equations In The Polynomial Class I. Bureau Sysmbol P2, Stud. Appl. Math. 104(2000)1–65.

Year 2013, Volume 3, Issue 2, 0 - 8, 01.12.2013

Abstract

References

  • [1] A. Karasu-Kalkanli, A. Karasu, A. Sakovich, et al., A New Integrable Generalization Of The Korteweg-de Vries Equation , J. Math. Phys., 49(2008)073516-073525.
  • [2] B. A. Kupershmidt, KdV6: An Integrable System, Phys. Lett. A 372(2008)2634–2639.
  • [3] B. A. Kupershmidt, A Super KdV Equation: An Integrable System, Phys. Lett. A 102(1984)213–215.
  • [4] Y. Q. Yao, Y. B. Zeng, The Bi-Hamiltonian Structure And New Solutions Of KdV6 Equation , Lett. Math. Phys., 86(2008)193-208.
  • [5] A. Ramani, B. Grammaticos, R. Willox, Bilinearize And Solutions Of The KdV6 , Anal. Appl., 6(2008)401-412.
  • [6] R. Hirota, Direct Methods In Soliton Theory, Springer, Berlin, 1980.
  • [7] A. M. Wazwaz, The Integrable KdV6 Equations: Multiple Soliton Solutions And Multiple Singular Soliton Solutions , Appl. Math. Comput. 204(2008)963–972.
  • [8] C. A. G´omez, A. Salas, The Cole-Hopf Transformation And Improved Tanh-coth Method Applied To New Integrable System (KdV6) , Appl. Math. Comput. 204(2008)957–962.
  • [9] J. B. Li, Y. Zhang, The Exact Traveling Wave Solutions To Two Integrable KdV6 Equations , Chin. Ann. Math. 33B(2)(2012)179–190.
  • [10] D. Kaup, On The Inverse Scattrin Problem For The Cubic Eigenvalue Problems Of The Class Ψ3x + 6QΨx + 6RΨ = λΨ, Stud. Appl. Math. 62(1980)189–216.
  • [11] M. C. Cosgrove, Higher-order Painleve Equations In The Polynomial Class I. Bureau Sysmbol P2, Stud. Appl. Math. 104(2000)1–65.

Details

Primary Language English
Journal Section Research Article
Authors

Zhao-hong SUN This is me
School of Computer Science, Zhongkai University Of Agriculture And Engineering, Guangzhou, guangdong 510225, P. R. China


Wei ZHANG This is me
School of Science, Yuxi Normal University, Yuxi, Yunnan 653100, P. R. China.

Publication Date December 1, 2013
Published in Issue Year 2013, Volume 3, Issue 2

Cite

Bibtex @ { twmsjaem761404, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2013}, volume = {3}, number = {2}, pages = {0 - 8}, title = {THE EXACT TRAVELING WAVE SOLUTIONS TO ONE INTEGRABLE KDV6 EQUATION}, key = {cite}, author = {Sun, Zhao-hong and Zhang, Wei} }