On soliton solutions of the modified equal width equation

Abstract

Purpose

The soliton solutions are obtained by using extended rational sin/cos and sinh-cosh method. The methods are powerful and have ease of use. Applying wave transformation to the nonlinear partial differential equations (NLPDEs) and the considered equation turns into a nonlinear differential equation (NODE). According to the methods, the solution sets of the NODE are supposed to the form of the rational terms as sinh/cosh and sin/cos and the trial solutions are substituted into the NODE. Collecting the same power of the trigonometric functions, a set of algebraic equations is derived.

Design/methodology/approach

The main purpose of this paper is to obtain soliton solutions of the modified equal width (MEW) equation. MEW is a form of regularized-long-wave (RLW) equation that represents one-dimensional wave propagation in nonlinear media with dispersion processes. This is also used to simulate the undular bore in a long shallow water canal.

Findings

Thus, the solution of the main PDE is reduced to the solution of a set of algebraic equations. In this paper, the kink, singular and singular periodic solitons have been successfully obtained.

Originality/value

Illustrative plots of the solutions have been presented for physical interpretation of the obtained solutions. The methods are powerful and might be used to solve a broad class of differential equations in real-life problems.

Citation

Onder, I., Cinar, M., Secer, A. and Bayram, M. (2023), "On soliton solutions of the modified equal width equation", Engineering Computations, Vol. 40 No. 5, pp. 1063-1083. https://doi.org/10.1108/EC-08-2022-0529