Riccati Equation Rational Expansion Method Research Articles

A new general algebraic method with symbolic computation to construct new exact analytical solution for a (2+1)-dimensional cubic nonlinear Schrödinger equation

Based on a new general ansätz, a new general algebraic method named improved Riccati equation rational expansion method is devised for constructing multiple nontravelling wave solutions for nonlinear partial differential equations . Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recover some known solutions, but also find some new and general solutions. With the aid of symbolic computation, we choose the (2 + 1)-dimensional cubic nonlinear Schrödinger equation to illustrate the method. As a result, six families of new exact analytical solutions for this equation are found, which include some new and more general exact rational form soliton-like solutions and triangular periodic-like solutions.

A new extended Riccati equation rational expansion method and its application

In this paper, a new extended Riccati equation rational expansion method is suggested to constructing multiple exact solutions for nonlinear evolution equations. The validity and reliability of the method is tested by its application to the dispersive long wave system and the Broer–Kaup–Kupershmidt system. The method can be applied to other nonlinear evolution equations in mathematical physics.

A multiple Riccati equations rational expansion method and novel solutions of the Broer–Kaup–Kupershmidt system

Abstract To construct exact solutions of nonlinear partial differential equation, a multiple Riccati equations rational expansion method (MRERE) is presented and a series of novel solutions of the Broer–Kaup–Kupershmidt system are found. The novel solutions obtained by MRERE method include solutions of hyperbolic (solitary) function and triangular periodic functions appearing at the same time.

Multiple Riccati equations rational expansion method and complexiton solutions of the Whitham–Broer–Kaup equation

A series of complexiton solutions of the Whitham–Broer–Kaup equation are found through a multiple Riccati equations rational expansion method presented in this Letter. Many new types of complexiton solutions such as various combination of trigonometric periodic and hyperbolic function solutions, various combination of trigonometric periodic and rational function solutions, various combination of hyperbolic and rational function solutions, etc., are obtained.

A NEW GENERAL ALGEBRAIC METHOD WITH SYMBOLIC COMPUTATION TO CONSTRUCT NEW TRAVELING SOLUTION FOR THE (1 +1)-DIMENSIONAL DISPERSIVE LONG WAVE EQUATION

A new algebraic method, named Riccati equation rational expansion (RERE) method, is devised for constructing multiple traveling wave solutions for nonlinear evolution equations (NEEs). With the aid of symbolic computation, we choose (1 +1)-dimensional dispersive long wave equation (DLWE) to illustrate our method. As a result, we obtain many types of solutions including rational form solitary wave solutions, triangular periodic wave solutions and rational wave solutions.

New Families of Rational Form Solitary Wave Solutions to(2+1)-Dimensional Broer–Kaup–Kupershmidt System

Taking the (2+1)-dimensionalBroer–Kaup–Kupershmidt system as a simple example, some familiesof rational form solitary wave solutions, triangular periodicwave solutions, and rational wave solutions are constructed byusing the Riccati equation rational expansion method presentedby us. The method can also be applied to solve more nonlinearpartial differential equation or equations.

A new Riccati equation rational expansion method and its application to (2+1)-dimensional Burgers equation

In this paper, we present a new Riccati equation rational expansion method to uniformly construct a series of exact solutions for nonlinear evolution equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recover some known solutions, but also find some new and general solutions. The solutions obtained in this paper include rational triangular periodic wave solutions, rational solitary wave solutions and rational wave solutions. The efficiency of the method can be demonstrated on (2 + 1)-dimensional Burgers equation.

A New Riccati Equation Rational Expansion Method and Its Application

A Riccati equation rational expansion (RERE) method is presented by a general ansatz, which is a direct and unified algebraic method for constructing multiple and more general travelling wave solutions of nonlinear partial differential equations. It can be implemented in a computer algebraic system. The proposed method is applied to consider the shallow long wave approximation equation and leads to a rich variety of exact solutions, including rational form solitary wave solutions, triangular periodic wave solutions and rational wave solutions.

A new general algebraic method with symbolic computation to construct new travelling wave solution for the (1 + 1)-dimensional dispersive long wave equation

With the aid of symbolic computation, a new algebraic method, named Riccati equation rational expansion (RERE) method, is devised for constructing multiple travelling wave solutions for nonlinear evolution equations (NEEs). Compared with most existing tanh methods for finding travelling wave solutions, the proposed method not only recover the results by most known algebraic methods, but also provides new and more general solutions. With the aid of symbolic computation, we choose (1 + 1)-dimensional dispersive long wave equation (DLWE) to illustrate our method. As a result, we obtain many types of solutions including rational form solitary wave solutions, triangular periodic wave solutions and rational wave solutions. The properties of the new solitary wave solutions are shown by some figures.