一类五阶非线性波方程的新精确解
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摘要
通过利用新的G展开法,并借助Mathematica计算软件,研究了一类五阶非线性波方程的精确解,获得了方程的含有多个任意参数的新的显式行波解,分别为三角函数解、双曲函数解、指数函数解,扩大了该类方程的解的范围.
A class of fifth-order nonlinear wave equations is studied by the new G-expansion method with the aid of computer symbolic systems Mathematica. As a result, some new exact solutions which involving parameters are obtained, these solutions contain the hyperbolic function solutions, the trigonometric function solutions and the exponential function solutions. The solutions of the fifth-order nonlinear wave equations have been enriched.
A class of fifth-order nonlinear wave equations is studied by the new G-expansion method with the aid of computer symbolic systems Mathematica. As a result, some new exact solutions which involving parameters are obtained, these solutions contain the hyperbolic function solutions, the trigonometric function solutions and the exponential function solutions. The solutions of the fifth-order nonlinear wave equations have been enriched.
引文
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[2] Wang M L, Zhang J L, Li X Z. Application of the(G'/G)-expansion to travelling wave solutions of the Broer-Kaup and the approximate long water wave equations[J]. Appl Math Comput, 2008,206:321-326.
[3] Li L X, Wang M L. The(G'/G)-expansion method and travelling wave solutions for a higher-order nonlinear schrodinger equation[J]. Appl Math Comput, 2009, 208:440-445.
[4] Triki H, Wazwaz A M. Traveling wave solutions for fifth-order KdV type equations with timedependent coefficients[J]. Communications in Nonlinear Science and Numerical Simulation, 2014,19(3):404-408.
[5] Sawada K, Kotera T. A method for finding N-soliton solutions for the KdV equation and KdV-like equation[J]. Progress of Theoretical Physics, 1974, 51(5):1355-1367.
[6] LI Ji-bin, QIAO Zhi-jun. Explicit solutions of the Kaup-Kupershmidt equation through the dynamical system approach[J]. Journal of Applied Analysis and Computation, 2011, 1(2):243-250.
[7] Kupershmidt B A. A super Korteweg-de Vires equation:an integrable system[J]. Physics Letters A, 1984,102(5/6):213-215.
[8] EI-Sayed S M. The decomposition method for studying the Klein-Gordon equation[J]. Chaos, Solitions&Fractals, 2003. 18:1025-1030.
[9] Caudrey P J, Eilbeck I C, Gibbon J D. The sine-Gordon equation as a model classical field theory[J].Nuovo Cimento, 1975, 25:497-511.
[10]邢秀芝,杨红艳,卜春霞.利用推广的(G'/G)展开法求解(2+1)维BBM方程[J].数学的实践与认识,2011, 41(16):240-243.
[11]陈自高.一类非线性发展方程的显式精确解[J].数学的实践与认识,2013, 43(9):201-207.
[12]刘绍庆,王淑勤,高国成.Wick型随机Kadomtsev-Petviashvili方程的精确解[J].数学的实践与认识,2014, 44(21):281-285.
[13]程万利,陈小刚,崔继峰.一类Benney-Kawahara-Lin方程的孤波解[J].数学的实践与认识,2014,44(17):228-235.
[14]刘转玲.mBBM方程的新解析解[J].数学的实践与认识,2013, 43(22):286-290.
[15]罗红英,刘俊,孙德贵,余晓婷.(2+1)维Boussinesq方程的呼吸波解[J].数学的实践与认识,2013,43(22):264-268.
[2] Wang M L, Zhang J L, Li X Z. Application of the(G'/G)-expansion to travelling wave solutions of the Broer-Kaup and the approximate long water wave equations[J]. Appl Math Comput, 2008,206:321-326.
[3] Li L X, Wang M L. The(G'/G)-expansion method and travelling wave solutions for a higher-order nonlinear schrodinger equation[J]. Appl Math Comput, 2009, 208:440-445.
[4] Triki H, Wazwaz A M. Traveling wave solutions for fifth-order KdV type equations with timedependent coefficients[J]. Communications in Nonlinear Science and Numerical Simulation, 2014,19(3):404-408.
[5] Sawada K, Kotera T. A method for finding N-soliton solutions for the KdV equation and KdV-like equation[J]. Progress of Theoretical Physics, 1974, 51(5):1355-1367.
[6] LI Ji-bin, QIAO Zhi-jun. Explicit solutions of the Kaup-Kupershmidt equation through the dynamical system approach[J]. Journal of Applied Analysis and Computation, 2011, 1(2):243-250.
[7] Kupershmidt B A. A super Korteweg-de Vires equation:an integrable system[J]. Physics Letters A, 1984,102(5/6):213-215.
[8] EI-Sayed S M. The decomposition method for studying the Klein-Gordon equation[J]. Chaos, Solitions&Fractals, 2003. 18:1025-1030.
[9] Caudrey P J, Eilbeck I C, Gibbon J D. The sine-Gordon equation as a model classical field theory[J].Nuovo Cimento, 1975, 25:497-511.
[10]邢秀芝,杨红艳,卜春霞.利用推广的(G'/G)展开法求解(2+1)维BBM方程[J].数学的实践与认识,2011, 41(16):240-243.
[11]陈自高.一类非线性发展方程的显式精确解[J].数学的实践与认识,2013, 43(9):201-207.
[12]刘绍庆,王淑勤,高国成.Wick型随机Kadomtsev-Petviashvili方程的精确解[J].数学的实践与认识,2014, 44(21):281-285.
[13]程万利,陈小刚,崔继峰.一类Benney-Kawahara-Lin方程的孤波解[J].数学的实践与认识,2014,44(17):228-235.
[14]刘转玲.mBBM方程的新解析解[J].数学的实践与认识,2013, 43(22):286-290.
[15]罗红英,刘俊,孙德贵,余晓婷.(2+1)维Boussinesq方程的呼吸波解[J].数学的实践与认识,2013,43(22):264-268.