扩展映射法与Boussinesq方程新的精确解

摘要

运用扩展映射法,结合辅助方程,利用计算机代数系统Mathematica求出Boussinesq方程一系列新的精确周期解,这些精确解在极限情况下(m→1)退化为相应的孤波解.该方法也可用来求解其他非线性演化方程,如Klein-Gordon方程和Benjamin方程等.%By making use of extended mapping method and auxiliary equation for finding new periodic wave solutions of nonlinear evolution equations in mathematical physics, we obtained some new periodic wave solutions for Boussinesq equation. When the modulus m → 1, these solutions degenerated into solitary wave solutions. This method also could be used to find new periodic wave solutions of other nonlinear evolution equations such as Klein-Gordon equation and Benjamin equation, etc.