2019Unpublished venueRequires access

Exp‐Function Method

Snehashish Chakraverty, Nisha Rani Mahato, Perumandla Karunakar, Tharasi Dilleswar Rao

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Abstract

This chapter explains the exp-function method by which one can find the solution (analytical/semi-analytical) of differential equations. This method was first proposed by He and Wu and was successfully applied to obtain the solitary and periodic solutions of nonlinear partial differential equations. Further, this method was used by many researchers for handling various other equations like stochastic equations, system of partial differential equations, nonlinear evaluation equation of high dimension, difference-differential equation, and nonlinear dispersive long-wave equation. This method is illustrated for partial differential equations as ordinary differential equations are straightforward while solving partial differential equations. The chapter considers a nonlinear partial differential equation to understand briefly the exp-function method. It solves two example problems to make the readers understand the exp-function method.

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What this paper is about

This chapter explains the exp-function method by which one can find the solution (analytical/semi-analytical) of differential equations. This method was first proposed by He and Wu and was successfully applied to obtain the solitary and periodic solutions of nonlinear partial differential equations. Further, this method was used by many researchers for handling various other equations like stochastic equations, system of partial differential equations, nonlinear evaluation equation of high dimension, difference-differential equation, and nonlinear dispersive long-wave equation. This method is illustrated for partial differential equations as ordinary differential equations are straightforward while solving partial differential equations. The chapter considers a nonlinear partial differential equation to understand briefly the exp-function method. It solves two example problems to make the readers understand the exp-function method.

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Available abstract

This chapter explains the exp-function method by which one can find the solution (analytical/semi-analytical) of differential equations. This method was first proposed by He and Wu and was successfully applied to obtain the solitary and periodic solutions of nonlinear partial differential equations. Further, this method was used by many researchers for handling various other equations like stochastic equations, system of partial differential equations, nonlinear evaluation equation of high dimension, difference-differential equation, and nonlinear dispersive long-wave equation. This method is illustrated for partial differential equations as ordinary differential equations are straightforward while solving partial differential equations. The chapter considers a nonlinear partial differential equation to understand briefly the exp-function method. It solves two example problems to make the readers understand the exp-function method.

Key concepts: Stochastic partial differential equation, First-order partial differential equation, Separable partial differential equation, Partial differential equation, Mathematics, Numerical partial differential equations, Nonlinear system, Method of characteristics

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