Abstract
In this paper, the generalized Jacobi elliptic functions expansion method with computerized symbolic computation are employed to investigate explicitly analytic solutions of the (N + 1)-dimensional generalized Boussinesq equation. The exact solutions to the equation are constructed analytically under certain circumstances, some of these solutions are degenerated to soliton-like solutions and trigonometric function solutions in the limit cases when the modulus of the Jacobi elliptic function solutions tends to 0 and 1, which shows that the applied method is more powerful and will be used in further works to establish more entirely new exact solutions for other kinds of higher-dimensional nonlinear partial differential equations in mathematical physics.
Highlights
In recent years, due to the wide applications of soliton theory in natural science, searching for exact soliton solutions of nonlinear evolution equations plays an important and significant role in the study on the dynamics of those phenomena [1,2]
The character feature of our method is that, without much extra effort, we can get series of exact solutions using a uniform way. Another advantage of our method is that it applies to general higher-dimensional nonlinear partial differential equations
We have found abundant new types of exact solutions for the (N + 1)-dimensional
Summary
Due to the wide applications of soliton theory in natural science, searching for exact soliton solutions of nonlinear evolution equations plays an important and significant role in the study on the dynamics of those phenomena [1,2]. We would like to discuss an (N + 1)-dimensional generalized Boussinesq equation by our generalized Jacobi elliptic functions expansion method [3]. The character feature of our method is that, without much extra effort, we can get series of exact solutions using a uniform way. Another advantage of our method is that it applies to general higher-dimensional nonlinear partial differential equations.
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