(1 + 1)维Benjiamin Omo方程的精确行波解研究
Study of the Exact Traveling Wave Solutions of (1+1) Dimensional Benjiamin Omo Equation
摘要: 通过行波变换,利用微分方程定性理论与动力系统分支方法,我们得到了(1 + 1)维Benjiamin Omo方程在不同参数形式下的线性波解。
Abstract:
Through the traveling wave transformation, by exploiting the qualitative theory of differential equations and the bifurcation method of dynamical systems, we obtained some nonlinearwave solutions for Benjiamin Omo equation under different parameter forms after travelingwave transformation.
参考文献
|
[1]
|
Benjiamin, T.B. (1967) Internal Waves of Permanent Formin Fluids of Great Depth. Journal of Fluid Mechanics, 29, 559-592. [Google Scholar] [CrossRef]
|
|
[2]
|
Davies, R.E. and Acrivos, A. (1967) Solitary Internal Waves Indeep Water. Journal of Fluid Mechanics, 29, 593-607. [Google Scholar] [CrossRef]
|
|
[3]
|
Ono, H. (1975) Algebraic Solitary Waves in Stratifiedfluids. Journal of the Physical Society of Japan, 39, 1082-1091. [Google Scholar] [CrossRef]
|
|
[4]
|
Wang, Z., Li, D.-S., Lu H.-F., et al. (2005). A Method for Constructing Exact Solutions and Application to Benjamin Ono Equation. Chinese Physics, 14, 2158-2158.[CrossRef]
|
|
[5]
|
Fu, Z. and Liu, S. (2003) The JEFE Method and Periodic Solutions of Two Kinds of Nonlinear Wave Equations. Communications in Nonlinear Science and Numerical Simulation, 8, 67-75. [Google Scholar] [CrossRef]
|
|
[6]
|
Xu, Z.H., Xian, D.Q. and Chen, H.L. (2010) New Periodic Solitary-Wave Solutions for the Benjiamin Ono Equation. Applied Mathematics and Computation, 215, 4439-4442. [Google Scholar] [CrossRef]
|
|
[7]
|
许瑞麟, 许晓革, 孟祥花. (1+1)维BenjiaminOno方程的精确显式解[J]. 北京信息科技大学学报(自然科学版), 2011, 26(3): 58-61.
|
|
[8]
|
杨娟, 冯庆江, 曾春花. 一类非线性数学物理方程的精确解[J]. 数学的实践与认识, 2018, 48(17): 309-313.
|
|
[9]
|
Wu, Y., Liu, Z.R. and Bai, C.Z. (2013) New Types of Nonlinear Waves and Bifurcation Phenomena in Schamel-Korteweg-de Vries Equation. Abstract and Applied Analysis, 2013, 1056-1083. [Google Scholar] [CrossRef]
|