Nonlocal symmetries and explicit solutions of the Boussinesq equation

Abstract

The nonlocal symmetry of the Boussinesq equation is obtained from the known Lax pair. The explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetry. Some other types of solutions, such as rational solutions and error function solutions, are given by using the fourth Painlevé equation with special values of the parameters. For some interesting solutions, the figures are given out to show their properties.

Keywords

Nonlocal symmetry / Lax pair / Prolonged system / Explicit solution

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