Sub-ODE's New Solutions and Their Applications to Two Nonlinear Partial Differential Equations with Higher-Order Nonlinear Terms

被引：0

作者：

Zhang Li-Hua ^{[1
,2
]}

He Jin-Yu ^{[3
]}

机构：

[1] Shandong Univ, Dept Math, Jinan 250100, Peoples R China

[2] Dezhou Univ, Dept Math, Dezhou 253023, Peoples R China

[3] Dezhou Univ, Dept Phys, Dezhou 253023, Peoples R China

来源：

COMMUNICATIONS IN THEORETICAL PHYSICS | 2009年 / 52卷 / 05期

关键词：

generalized KdV-mKdV equation; generalized Zakharov-Kuznetsov equation; the sub-ODE methods; symbolic computation; higher-order nonlinear terms; TRAVELING-WAVE SOLUTIONS; KDV-MKDV EQUATION; VARIABLE-COEFFICIENTS; ALGEBRAIC-METHOD; CAMASSA-HOLM;

D O I：

暂无

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In the present paper, with the aid of symbolic computation, families of new nontrivial solutions of the first-order sub-ODE F'2 = AF(2) + BF2+p + CF2+2p (where F' = dF/d xi, p > 0) are obtained. To our best knowledge, these nontrivial solutions have not been found in [X.Z. Li and M.L. Wang, Phys. Lett. A 361 (2007) 115] and [S. Zhang, W. Wang, and J.L. Tong, Phys. Lett. A 372 (2008) 3808] and other existent papers until now. Using these nontrivial solutions, the sub-ODE method is described to construct several kinds of exact travelling wave solutions for the generalized KdV-mKdV equation with higher-order nonlinear terms and the generalized ZK equation with higher-order nonlinear terms. By means of this method, many other physically important nonlinear partial differential equations with nonlinear terms of any order can be investigated and new nontrivial solutions can be explicitly obtained with the help of symbolic computation system Maple or Mathematica.

引用

页码：773 / 778

页数：6

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