A generalized auxiliary equation method and its application to (2+1)-dimensional Korteweg-de Vries equations

作者：Zhang Sheng^*

来源：Computers & Mathematics with Applications, 2007, 54(7-8): 1028-1038.

DOI：10.1016/j.camwa.2006.12.046

• generalized auxiliary equation method
• soliton-like solutions
• triangular-like solutions
• Jacobi elliptic wave function-like solutions
• Weierstrass elliptic doubly-like periodic solutions

A generalized auxiliary equation method is proposed for constructing more general exact solutions of nonlinear partial differential equations. With the aid of symbolic computation, we choose the (2 + 1)-dimensional Korteweg-de Vries equations to illustrate the validity and advantages of this method. As a result, many new and more general exact non-travelling wave and coefficient function solutions are obtained, which include soliton-like solutions, triangular-like solutions, single and combined non-degenerate Jacobi elliptic wave function-like solutions and Weierstrass elliptic doubly-like periodic solutions.

• 出版日期2007-10
• 单位渤海大学