Complex solutions of the time fractional Gross-Pitaevskii (GP) equation with external potential by using a reliable method

In this article, modified (G\u27/G )-expansion method is presented to establish the exact complex solutions of the time fractional Gross-Pitaevskii (GP) equation in the sense of the conformable fractional derivative. This method is an effective method in finding exact traveling wave solutions of nonlinear evolution equations (NLEEs) in mathematical physics. The present approach has the potential to be applied to other nonlinear fractional differential equations. Based on two transformations, fractional GP equation can be converted into nonlinear ordinary differential equation of integer orders. In the end, we will discuss the solutions of the fractional GP equation with external potentials

Exact Solutions of Two Nonlinear Space-time Fractional Differential Equations by Application of Exp-function Method

In this paper, we discuss on the exact solutions of the nonlinear space-time fractional Burgerlike equation and also the nonlinear fractional fifth-order Sawada-Kotera equation with the expfunction method.We use the functional derivatives in the sense of Riemann-Jumarie derivative and fractional convenient variable transformation in this study. Further, we obtain some exact analytical solutions including hyperbolic function

Exact Soliton Solutions for Second-Order Benjamin-Ono Equation

The homogeneous balance method is proposed for seeking the travelling wave solutions of the second-order Benjamin-Ono equation. Many exact traveling wave solutions of second-order Benjamin-Ono equation, which contain soliton like and periodic-like solutions are successfully obtained. This method is straightforward and concise, and it may also be applied to other nonlinear evolution equations

Exact Travelling Wave Solutions of the Coupled Klein-Gordon Equation by the Infinite Series Method

In this paper, we employ the infinite series method for travelling wave solutions of the coupled Klein-Gordon equations. Based on the idea of the infinite series method, a simple and efficient method is proposed for obtaining exact solutions of nonlinear evolution equations. The solutions obtained include solitons and periodic solutions

Application of Bernoulli Sub-ODE Method For Finding Travelling Wave Solutions of Schrodinger Equation Power Law Nonlinearity

In this paper, the exact travelling wave solution of the Schr¨odinger equation with power law nonlinearity is studied by the Sub-ODE method. It is shown that the method is one of the most effective approaches for finding exact solutions of nonlinear differential equations

Application of Reduced Differential Transform Method for Solving Two-dimensional Volterra Integral Equations of the Second Kind

In this paper, we propose new theorems of the reduced differential transform method (RDTM) for solving a class of two-dimensional linear and nonlinear Volterra integral equations (VIEs) of the second kind. The advantage of this method is its simplicity in using. It solves the equations straightforward and directly without using perturbation, Adomian’s polynomial, linearization or any other transformation and gives the solution as convergent power series with simply determinable components. Also, six examples and numerical results are provided so as to validate the reliability and efficiency of the method

Study on Solving Two-dimensional Linear and Nonlinear Volterra Partial Integro-differential Equations by Reduced Differential Transform Method

In this article, we study on the analytical and numerical solution of two-dimensional linear and nonlinear Volterra partial integro-differential equations with the appropriate initial condition by means of reduced differential transform method. The advantage of this method is its simplicity in using, it solves the problem directly without the need for linearization, perturbation, or any other transformation and gives the solution in the form of convergent power series with elegantly computed components. The validity and efficiency of this method are illustrated by considering five computational examples

New Exact Solutions of some Nonlinear Partial Differential Equations by the First Integral Method

The first integral method is an efficient method for obtaining exact solutions of nonlinear partial differential equations. The efficiency of the method is demonstrated by applying it for two selected equations. This method can be applied to nonintegrable equations as well as to integrable ones

Application of the Extended G\u27/G-expansion Method to the Improved Eckhaus Equation

In this paper, the extended (G\u27/G)-expansion method is used to seek more general exact solutions of the improved Eckhaus equation and the (2+1)-dimensional improved Eckhaus equation. As a result, hyperbolic function solutions, trigonometric function solutions and rational function solutions with free parameters are obtained. When the parameters are taken as special values the solitary wave solutions are also derived from the traveling wave solutions. Moreover, it is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations in mathematical physics

Exact solutions of (2+1)-dimensional nonlinear evolution equations by using the extended tanh method,

Abstract: In this paper, the extended tanh method is used to construct exact solutions of the generalized Kadomtsev-Petviashvili (gKP) equation in the for