Exact solutions of the nonlinear Schrödinger equation by the first integral method

AbstractThe first integral method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. In this paper, the first integral method is used to construct exact solutions of the nonlinear Schrödinger equation

Solutions of nonlinear fractional coupled Hirota-Satsuma-KdV Equation

Our interest in the present work is in implementing the FPSM to stress it power in handing the nonlinear fractional coupled Hirota-Satsuma-KdV Equation. The approximate analytical solution of this type equations are obtained

Exact Solutions of the Generalized- Zakharov (GZ) Equation by the Infinite Series Method

The infinite series method is an efficient method for obtaining exact solutions of some nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. In this paper, the direct algebraic method is used to construct new exact solutions of generalized- Zakharov equation

Traveling Wave Solutions of ZK-BBM Equation Sine-Cosine Method

Travelling wave solutions are obtained by using a relatively new technique which is called sine-cosine method for ZK-BBM equations. Solution procedure and obtained results re-confirm the efficiency of the proposed scheme

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

Exact Travelling Wave Solutions for Konopelchenko-Dubrovsky Equation by the First Integral Method

In this paper, the first integral method is used to construct exact travelling wave solutions of Konopelchenko-Dubrovsky equation. The first integral method is algebraic direct method for obtaining exact solutions of nonlinear partial differential equations. This method can be applied to non-integrable equations as well as to integrable ones. This method is based on the theory of commutative algebra

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

Two Reliable Methods for Solving the Modified Improved Kadomtsev-Petviashvili Equation

In this paper, the tanh-coth method and the extended (G\u27/G)-expansion method are used to construct exact solutions of the nonlinear Modified Improved Kadomtsev-Petviashvili (MIKP) equation. These methods transform nonlinear partial differential equation to ordinary differential equation and can be applied to nonintegrable equation as well as integrable ones. It has been shown that the two methods are direct, effective and can be used for many other nonlinear evolution equations in mathematical physics