Nonlocal symmetry and interaction solutions for the new (3+1)-dimensional integrable Boussinesq equation

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, PR China.

^* Corresponding author: hhengchun@163.com

Received: 10 August 2021
Accepted: 28 December 2021

Abstract

The nonlocal symmetry of the new (3+1)-dimensional Boussinesq equation is obtained with the truncated Painlevé method. The nonlocal symmetry can be localized to the Lie point symmetry for the prolonged system by introducing auxiliary dependent variables. The finite symmetry transformation related to the nonlocal symmetry of the integrable (3+1)-dimensional Boussinesq equation is studied. Meanwhile, the new (3+1)-dimensional Boussinesq equation is proved by the consistent tanh expansion method and many interaction solutions among solitons and other types of nonlinear excitations such as cnoidal periodic waves and resonant soliton solution are given.