Abstract
By using Jacobi elliptic function expansion method, several kinds of travelling wave solutions of Nonlinear Vakhnenko equation are obtained in this paper. As a result, some new forms of traveling wave solutions of the equation are shown, and the numerical simulation with different parameters for the new forms solutions are given.
Highlights
The nature of the world is known by people step by step with many powerful methods
By using Jacobi elliptic function expansion method, several kinds of travelling wave solutions of Nonlinear Vakhnenko equation are obtained in this paper
Nonlinear Vakhnenko equation is a kind of nonlinear partial differential equation, which is proposed to describe long waves of small amplitudes broadcasting in nonlinear dispersive media
Summary
The nature of the world is known by people step by step with many powerful methods. Solving linear equation is the beginning of the process, the results do not well agree with the solution of the linear equation. People overcome the difference and find the nonlinear equation, which is used to describe many phenomena in various physics fields. Nonlinear Vakhnenko equation is a kind of nonlinear partial differential equation, which is proposed to describe long waves of small amplitudes broadcasting in nonlinear dispersive media. With deeply studying the relation of nature, many powerful methods appear [1]-[7]. The nonlinear Vakhnenko equation is investigated in many papers [8] [9] [10] [11]; some new solutions in the form of Jacobi elliptic function are given in this paper, which enrich the kinds of the solution.
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