Construction of doubly-periodic solutions to nonlinear partial differential equations using improved Jacobi elliptic function expansion method and symbolic computation

• 来源期刊: 中国物理（英文版）
• 关键词: Jacobi elliptic function method doubly-periodic solutions Zakharov-Kuznetsov equation
• 年，卷（期）: 2006,（10）
• 页码范围: 2202-2209
• 页数: 8页
• 语种: 英文

摘要

Some doubly-periodic solutions of the Zakharov-Kuznetsov equation are presented. Our approach is to introduce an auxiliary ordinary differential equation and use its Jacobi elliptic function solutions to construct doubly-periodic solutions of the Zakharov-Kuznetsov equation, which has been derived by Gottwald as a two-dimensional model for nonlinear Rossby waves. When the modulus k→1, these solutions reduce to the solitary wave solutions of the equation.