Exact Solutions to a Combined sinh-cosh-Gordon Equation

• 来源期刊: 理论物理通讯(英文版)
• 学科: 数学
• 关键词: 偏微分方程 双曲正弦 双曲余弦 精确解 ODE方法 非线性方程 常微分方程 函数变换
• 年，卷（期）: 2010,（10）
• 页码范围: 599-602
• 页数: 4页
• 分类号: O175.2 TN241
• 语种: 英文

摘要

Based on a transformed Painleve property and the variable separated ODE method, a function transformationmethod is proposed to search for exact solutions of some partial differential equations (PDEs) with hyperbolic orexponential functions.This approach provides a more systematical and convenient handling of the solution process of thiskind of nonlinear equations.Its key point is to eradicate the hyperbolic or exponential terms by a transformed Painleveproperty and reduce the given PDEs to a variable-coefficient ordinary differential equations, then we seek for solutions tothe resulting equations by some methods.As an application, exact solutions for the combined sinh-cosh-Gordon equationare formally derived.