General Solutions Of Nonlinear Equations Research Articles

A modified extended method to find a series of exact solutions for a system of complex coupled KdV equations

In this paper an algebraic method is devised to uniformly construct a series of complete new exact solutions for general nonlinear equations. For illustration, we apply the modified proposed method to revisit a complex coupled KdV system and successfully construct a series of new exact solutions including the soliton solutions and elliptic doubly periodic solutions.

A series of new exact solutions for a complex coupled KdV system

In this paper an algebraic method is devised to uniformly construct a series of exact solutions for general nonlinear equations. Compared with the existing tanh methods and Jacobi function method, the proposed method gives more general exact solutions without much extra effort. More importantly, the method provides a guideline for the classification of the solutions based on the given parameters. For illustration, we apply the proposed method to revisit a complex coupled KdV system and successfully construct a series of new exact solutions including the soliton solutions and elliptic doubly periodic solutions.

Soliton solutions and doubly periodic wave solutions for a new generalized Hirota–Satsuma coupled system

In this paper, a new algebraic method with symbolic computation is presented to uniformly construct a series of exact solutions for general nonlinear equations. Compared with most existing tanh methods, the proposed method not only gives new and more general solutions, but also provides a guideline to classify the various types of the solutions according to the values of some parameters. For illustration, we apply the proposed method to solve a new generalized Hirota–Satsuma coupled system and explicitly construct a series of exact solutions which include the soliton solutions and elliptic doubly periodic solutions as special cases. In addition, the links among our proposed method, the tanh method and the extended method are also clarified generally.

Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics

In this paper, we devise a new unified algebraic method to construct a series of explicit exact solutions for general nonlinear equations. Compared with most existing methods such as tanh method, Jacobi elliptic function method and homogeneous balance method, the proposed method not only gives new and more general solutions, but also provides a guideline to classify the various types of the solutions according to the values of some parameters. The solutions obtained in this paper include (a) polynomial solutions, (b) exponential solutions, (c) rational solutions, (d) triangular periodic wave solutions, (e) hyperbolic, and soliton solutions, (f) Jacobi, and Weierstrass doubly periodic wave solutions. The efficiency of the method can be demonstrated on a large variety of nonlinear equations such as those considered in this paper, combined KdV–MKdV, Camassa–Holm, Kaup–Kupershmidt, Jaulent–Miodek, (2+1)-dimensional dispersive long wave, new (2+1)-dimensional generalized Hirota, (2+1)-dimensional breaking soliton and double sine-Gordon equations. In addition, the links among our proposed method, the tanh method, the extended method and the Jacobi function expansion method are also clarified generally.

A new algebraic method for finding the line soliton solutions and doubly periodic wave solution to a two-dimensional perturbed KdV equation

A new algebraic method is devised to obtain a series of exact solutions for general nonlinear equations. Compared with the most existing tanh methods, the proposed method gives new and more general solutions. More importantly, the method provides a guideline to classify the various types of the solution according to some parameters. For illustration, we apply the method to solve a new two-dimensional perturbed KdV equation and successfully construct the various kind of exact solutions including line soliton solutions, rational solutions, triangular periodic solutions, Jacobi, and Weierstrass doubly periodic solutions.

General solutions of nonlinear equations in the geometric theory of the relativistic string

General solutions for the system of nonlinear equations in the second order partial derivatives with two independent variables are obtained. They determine the basic differential forms of the two-dimensional minimal surface embedded inton-dimensional pseudo-Euclidean space.

General solutions of nonlinear equations in the theory of minimal surfaces

General solutions of nonlinear equations in the theory of minimal surfaces