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.
Highlights
The study of nonlinear integrable systems is one of the most important subjects in the nonlinear science
Abundant interaction solutions among solitons and different waves including periodic cnoidal waves, Painleve waves and Boussinesq waves for many integrable systems have been obtained by nonlocal symmetry reduction and the consistent tanh expansion method related to the Painleve analysis [2, 3, 9, 13, 20]
In order to solve the initial value problem related to the nonlocal symmetry, the equation (1.1) is extended to the enlarged one by introducing the dependent variables
Summary
The study of nonlinear integrable systems is one of the most important subjects in the nonlinear science. Abundant interaction solutions among solitons and different waves including periodic cnoidal waves, Painleve waves and Boussinesq waves for many integrable systems have been obtained by nonlocal symmetry reduction and the consistent tanh expansion method related to the Painleve analysis [2, 3, 9, 13, 20]. We give the nonlocal symmetry and corresponding finite symmetry transformation for the new (3+1)-dimensional Boussinesq equation (1.1) are discussed based on the truncated Painleve expansion. 3. Consistent tanh expansion method and interaction solutions of the new (3+1)-dimensional Boussinesq equation.
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