Application of Exp-function method to Riccati equation and new exact solutions with three arbitrary functions of Broer-Kaup-Kupershmidt equations

In this Letter, the Exp-function method is used to seek generalized solitonary solutions of Riccati equation. Based on the Riccati equation and its generalized solitonary solutions, new exact solutions with three arbitrary functions of the (2+1)-dimensional Broer-Kaup-Kupershmidt equations are obtained. It is shown that the Exp-function method provides a straightforward and important mathematical tool for nonlinear evolution equations in mathematical physics.     

A novel approach for solving the Fisher equation using Exp-function method

In this Letter, Exp-function method is employed to obtain traveling wave solutions of the Fisher equation. It is shown that, on this example, the Exp-function method is easy to implement and concise method for nonlinear evolution equations in mathematical physics.     

Exp-function method for N-soliton solutions of nonlinear evolution equations in mathematical physics

In this Letter, the Exp-function method is generalized to construct N-soliton solutions of a KdV equation with variable coefficients. As a result, 1-soliton, 2-soliton and 3-soliton solutions are obtained, from which the uniform formula of N-soliton solutions is derived. It is shown that the Exp-function method may provide us with a straightforward and effective mathematical tool for generating N-soliton solutions of nonlinear evolution equations in mathematical physics.     

New solitonary solutions for the MBBM equations using Exp-function method

In this Letter we use the Exp-function method for analytic treatment for the modified Benjamin-Bona-Mahony equations. New solitonary solutions are formally derived. The change of the parameters, that will drastically change the characteristics of the equations, is examined. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving high-dimensional nonlinear evolutions in mathematical physics.     

New periodic wave solutions via Exp-function method

The Exp-function method with the aid of symbolic computational system is used to obtain the generalized solitary solutions and periodic solutions for nonlinear evolution equations arising in mathematical physics, namely, nonlinear partial differential (BBMB) equation, generalized RLW equation and generalized shallow water wave equation. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving other nonlinear evolution equations arising in mathematical physics.     

Application of Exp-function method for a system of three component-Schrödinger equations

An algorithm is devised for deriving exact traveling wave solutions of a three-component system of nonlinear Schrödinger (NLS) equations by means of Exp-function method. This method was previously applied to nonlinear partial differential equations (NLPDEs) or two coupled NLPDEs, here it is applied to three coupled NLPDES. This work continues to reinforce the idea that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear partial differential equations.     

Application of Exp-function method to Symmetric Regularized Long Wave (SRLW) equation

In this Letter, the Exp-function method with the aid of Maple is used to obtain generalized soliton solution and periodic solution with some free parameters for the Symmetric Regularized Long Wave (SRLW) equation. Suitable choice of parameters in the generalized solution leads to Darwish's solution [A.A. Darwish, A. Ramady, Chaos Solitons Fractals 33 (4) (2007) 1263]. The result shows that Exp-function method is a powerful mathematical tool for solving nonlinear equations arising in mathematical physics.     

A reliable treatment for nonlinear Schrödinger equations

Exp-function method is used to find a unified solution of nonlinear wave equation. Nonlinear Schrödinger equations with cubic and power law nonlinearity are selected to illustrate the effectiveness and simplicity of the method. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving nonlinear equation.     

Exact solutions for nonlinear evolution equations using Exp-function method

In this Letter, the Exp-function method is used to construct solitary and soliton solutions of nonlinear evolution equations. The Klein-Gordon, Burger-Fisher and Sharma-Tasso-Olver equations are chosen to illustrate the effectiveness of the method. The method is straightforward and concise, and its applications are promising. The Exp-function method presents a wider applicability for handling nonlinear wave equations.     

Application of Exp-Function Method to Discrete Nonlinear Schrödinger Lattice Equation with Symbolic Computation

In this paper, we present an extended Exp-function method to differential-difference equation(s). With the help of symbolic computation, we solve discrete nonlinear Schrödinger lattice as an example, and obtain a series of general solutions in forms of Exp-function.     

Generalized solitary solution and compacton-like solution of the Jaulent-Miodek equations using the Exp-function method

A new generalized solitary solution of the Jaulent-Miodek equations is obtained using the Exp-function method. By a transformation, the solitary solution can be easily converted into a generalized compacton-like solution. The free parameters in the obtained generalized solutions might imply some meaningful results in physical process.     

Some Remarks on Exp-Function Method and Its Applications

Recently, many important nonlinear partial differential equations arising in the applied physical and mathematical sciences have been tackled by a popular approach, the so-called Exp-function method. In this paper, we present some shortcomings of this method by analyzing the results of recently published papers. We also discuss the possible improvement of the effectiveness of the method.     

Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method

Based on the Exp-function method, exact solutions for some nonlinear evolution equations are obtained. The KdV equation, Burgers' equation and the combined KdV–mKdV equation are chosen to illustrate the effectiveness of the method.     

Some Remarks on Exp-Function Method and Its Applications-A Supplement

Recently, the authors of [Commun. Theor. Phys. 56 (2011) 397] made a number of useful observations on Exp-function method. In this study, we focus on another vital issue, namely, the misleading results of double Exp-function method.     

Exact solutions of stochastic fractional Korteweg de–Vries equation with conformable derivatives

We deal with the Wick-type stochastic fractional Korteweg de–Vries(KdV) equation with conformable derivatives.With the aid of the Exp-function method, white noise theory, and Hermite transform, we produce a novel set of exact soliton and periodic wave solutions to the fractional KdV equation with conformable derivatives. With the help of inverse Hermite transform, we get stochastic soliton and periodic wave solutions of the Wick-type stochastic fractional KdV equation with conformable derivatives. Eventually, by an application example, we show how the stochastic solutions can be given as Brownian motion functional solutions.     

Some Remarks on Exp-Function Method and Its Applications-A Supplement

Recently, the authors of [Commun. Theor. Phys. 56 （2011） 397] made a number of useful observations on Exp-function method. In this study, we focus on another vital issue, namely, the misleading results of double Exp-function method.     

Variable-coefficient extended mapping method for nonlinear evolution equations

In this Letter, a variable-coefficient extended mapping method is proposed to seek new and more general exact solutions of nonlinear evolution equations. Being concise and straightforward, this method is applied to the mKdV equation with variable coefficients and (2+1)-dimensional Nizhnik-Novikov-Veselov equations. As a result, many new and more general exact solutions are obtained including Jacobi elliptic function solutions, hyperbolic function solutions and trigonometric function solutions. It is shown that the proposed method provides a very effective and powerful mathematical tool for solving a great many nonlinear evolution equations in mathematical physics.     

Classification of traveling wave solutions for time-fractional fifth-order KdV-like equation

In this paper, we studied time-fractional nonlinear partial differential equations to reach their some solutions. There are lots of explicit and analytic methods in the literature. We used Kudryashov, Exp-function, and Jacobi elliptic rational expansion methods. By using these methods, we get some solutions of time-fractional fifth-order KdV-like equation.     

Application of Exp-Function Method to Discrete Nonlinear SchrSdinger Lattice Equation with Symbolic Computation

In this paper, we present an extended Exp-function method to differential-difference equation（s）. With the help of symbolic computation, we solve discrete nonlinear Schrodinger lattice as an example, and obtain a series of general solutions in forms of Exp-function.     

Construction of new exact solutions to time-fractional two-component evolutionary system of order 2 via different methods

This paper is concerned with the applications of five different methods including the sub-equation method, the tanh method, the modified Kudryashov method, the \(\left( \frac{G'}{G}\right)\)-expansion method and the Exp-function method to construct exact solutions of time-fractional two-component evolutionary system of order 2. We first convert this type of fractional equations to the nonlinear ordinary differential equations by means of fractional complex transform. Then, the five methods are adopted to solve the nonlinear ordinary differential equations. As a result, some new exact solutions are obtained. It is also shown that each of the considered methods can be used as an alternative for solving fractional differential equations.