中国物理B ›› 2006, Vol. 15 ›› Issue (10): 2202-2209.doi: 10.1088/1009-1963/15/10/003
智红燕1, 张鸿庆1, 赵雪芹2
Zhao Xue-Qin(赵雪芹)a)b)†, Zhi Hong-Yan(智红燕)a), and Zhang Hong-Qing(张鸿庆)a)
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 \rightarrow 1, these solutions reduce to the solitary wave solutions of the equation.
中图分类号: (Partial differential equations)