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2014•SpringerPlusOpen access

Exact traveling wave solutions of modified KdV–Zakharov–Kuznetsov equation and viscous Burgers equation

Md Hamidul Islam, Kamruzzaman Khan, M. Ali Akbar, Md. Abdus Salam

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Abstract

ABSTRACT: Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters. MATHEMATICS SUBJECT CLASSIFICATION: 35C07; 35C08; 35P99.

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ABSTRACT: Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters. MATHEMATICS SUBJECT CLASSIFICATION: 35C07; 35C08; 35P99.

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Available abstract

ABSTRACT: Mathematical modeling of many physical systems leads to nonlinear evolution equations because most physical systems are inherently nonlinear in nature. The investigation of traveling wave solutions of nonlinear partial differential equations (NPDEs) plays a significant role in the study of nonlinear physical phenomena. In this article, we construct the traveling wave solutions of modified KDV-ZK equation and viscous Burgers equation by using an enhanced (G '/G) -expansion method. A number of traveling wave solutions in terms of unknown parameters are obtained. Derived traveling wave solutions exhibit solitary waves when special values are given to its unknown parameters. MATHEMATICS SUBJECT CLASSIFICATION: 35C07; 35C08; 35P99.

Key concepts: Traveling wave, Burgers' equation, Korteweg–de Vries equation, Nonlinear system, Partial differential equation, Kadomtsev–Petviashvili equation, Mathematical analysis, Physics

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