TY - JOUR T1 - THE EXACT TRAVELING WAVE SOLUTIONS TO ONE INTEGRABLE KDV6 EQUATION AU - Sun, Zhao-hong AU - Zhang, Wei PY - 2013 DA - December JF - TWMS Journal of Applied and Engineering Mathematics JO - JAEM PB - Işık University Press WT - DergiPark SN - 2146-1147 SP - 0 EP - 8 VL - 3 IS - 2 LA - en AB - 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. KW - KdV6 equation KW - exact traveling wave solution KW - solitary wave solution CR - [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. CR - [2] B. A. Kupershmidt, KdV6: An Integrable System, Phys. Lett. A 372(2008)2634–2639. CR - [3] B. A. Kupershmidt, A Super KdV Equation: An Integrable System, Phys. Lett. A 102(1984)213–215. CR - [4] Y. Q. Yao, Y. B. Zeng, The Bi-Hamiltonian Structure And New Solutions Of KdV6 Equation , Lett. Math. Phys., 86(2008)193-208. CR - [5] A. Ramani, B. Grammaticos, R. Willox, Bilinearize And Solutions Of The KdV6 , Anal. Appl., 6(2008)401-412. CR - [6] R. Hirota, Direct Methods In Soliton Theory, Springer, Berlin, 1980. CR - [7] A. M. Wazwaz, The Integrable KdV6 Equations: Multiple Soliton Solutions And Multiple Singular Soliton Solutions , Appl. Math. Comput. 204(2008)963–972. CR - [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. CR - [9] J. B. Li, Y. Zhang, The Exact Traveling Wave Solutions To Two Integrable KdV6 Equations , Chin. Ann. Math. 33B(2)(2012)179–190. CR - [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. CR - [11] M. C. Cosgrove, Higher-order Painleve Equations In The Polynomial Class I. Bureau Sysmbol P2, Stud. Appl. Math. 104(2000)1–65. UR - https://dergipark.org.tr/en/pub/twmsjaem/issue//761404 L1 - https://dergipark.org.tr/en/download/article-file/1179915 ER -