A new generalized expansion method and its application in finding explicit exact solutions for a generalized variable coefficients KdV equation

作者：Sabry R^*; Zahran MA; Fan EG

来源：Physics Letters A, 2004, 326(1-2): 93-101.

DOI：10.1016/j.physleta.2004.04.002

• generalized expansion method
• generalized KdV equation with variable coefficients
• cylindrical KdV equation
• solitary wave solutions
• Jacobi and Weierstrass doubly periodic wave solutions
• symbolic computation

A generalized expansion method is proposed to uniformly construct a series of exact solutions for general variable coefficients non-linear evolution equations. The new approach admits the following types of solutions (a) polynomial solutions, (b) exponential solutions, (c) rational solutions, (d) triangular periodic wave solutions, (e) hyperbolic and solitary wave solutions and (f) Jacobi and Weierstrass doubly periodic wave solutions. The efficiency of the method has been demonstrated by applying it to a generalized variable coefficients KdV equation. Then, new and rich variety of exact explicit solutions have been found.

• 出版日期2004-5-31
• 单位复旦大学