Abstract
Trial equation method is a powerful tool for obtaining exact solutions of nonlinear differential equations. In this paper, the improved Boussinesq is reduced to an ordinary differential equation under the travelling wave transformation. Trial equation method and the theory of complete discrimination system for polynomial are used to establish exact solutions of the improved Boussinesq equation.
Highlights
In every field of engineering technology, science research, natural world and human society activities, nonlinear phenomena occupy an important position
Boussinesq-type equations are frequently used in computer models for the simulation of water waves in shallow seas and harbours
The objective of this paper is to apply Liu’s method and the theory of complete discrimination system for polynomial [12,13,14,15,16] to find the exact solutions of the nonlinear differential equation
Summary
In every field of engineering technology, science research, natural world and human society activities, nonlinear phenomena occupy an important position. The investigation of exact solutions of nonlinear evolution equations helps us understand these phenomena better. With the development of soliton theory and the application of computer symbolic system such as Matlab and Mathematica, many powerful methods for obtaining exact solutions of nonlinear evolution equations are presented, such as the inverse scattering method [1], Hirotas bilinear transformation [2,3], the tanh method [4], sine-cosine method [5], homogeneous balance method [6,7], expfunction method [8], and so on. The objective of this paper is to apply Liu’s method and the theory of complete discrimination system for polynomial [12,13,14,15,16] to find the exact solutions of the nonlinear differential equation
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