Numerical solitons of generalized Korteweg-de Vries equations

摘要

We propose a numerical method for finding solitary wave solutions of generalized Korteweg-de Vries equations by solving the nonlinear eigenvalue problem on an unbounded domain. The artificial boundary conditions are obtained to make the domain finite. We specially discuss the soliton solutions of the K(m, n) equation and KdV–K(m, n) equation. Furthermore for the mixed models of linear and nonlinear dispersion, the collision behaviors of soliton–soliton and soliton–antisoliton are observed.