A new soliton solution and periodic solution of a nonlinear dispersion-dissipation equation

solitary solution;  periodic solution;  Computer Algebra System

The truncation auxiliary function method for finding the accurate solution of nonlinear partial differential equations is briefly introduced, which is concise and effective. Using the truncation auxiliary function method, with the help of the computer algebra system Mathematica, a new nonlinear dispersion-dissipation equation for describing the evolution of ionic weak nonlinear ion acoustic waves composed of cold ions and hot electrons is obtained, and new soliton solutions, periodic solutions and several sets of steady-state solutions are obtained. These solutions contain arbitrary constants, and when any constant takes a specific value, the computer algebra system Mathematica gives a graph of the partial solution.