一类非线性演化方程新的显式行波解

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基金项目: 国家重点基础研究发展规划项目(G1998030600);国家自然科学基金资助项目(10072013);高等学校博士学科点专项科研基金资助

New Explicit and Exact Travelling Wave Solutions for a Class of Nonlinear Evolution Equations

Department of Mathematics, Dalian University of Technology, Dalian 116024, P. R. China

摘要: 借助Mathematica软件和吴方法,采用双曲函数法,获得了一类非线性演化方程u_tt+au_xx+bu+cu²+du³=0的多组行波解,其中包括周期解与孤子解.这种方法也适用于其他非线性方程或方程组.
- 方程 /
- 周期解 /
- 孤波解
Abstract: With the help of Mathematica, many travelling wave solutions for a class of nonlinear evolution equations u_tt+au_xx+bu+cu²+du³=0 are obtained by using hyperbola function method and Wuelimation method, which include new travelling wave solutions, periodicl solutions and kink soliton solutions. Some equations such as Duffing equation, sin-Gordon equation, φ⁴ and Klein-Gordon equation are particular cases of the evolution equations. The method can also be applied to other nonlinear equations.
- equation /
- periodic solution /
- solitary wave solution

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