Symbolic computation and construction of exact traveling wave solutions to the variant Boussinesq equations

摘要

In this paper, the auxiliary equation method is used to seek exact solutions for the the variant Boussinesq equations. As a result, some traveling wave solutions in terms of theta functions are successfully obtained with the aid of symbolic computation for the first time. It is shown that the auxiliary equation method is a very effective and powerful mathematical tool for solving nonlinear evolution equations in mathematics and physics.