Dimensional potential-YTSF Equation Research Articles

A new variable coefficient Korteweg-de Vries equation-based sub-equation method and its application to the (3 + 1)-dimensional potential-YTSF equation

With the aid of Maple, we present variable coefficient Korteweg-de Vries equation-based sub-equation method. The key idea of our method is to take advantage of the variable coefficient Korteweg-de Vries equation and its various solutions to generate various solutions of nonlinear evolution equations. The efficiency of the method can be demonstrated on the (3 + 1)-dimensional potential-YTSF equation and we construct successfully its new styles of solutions.

Non-travelling wave solutions to a (3+1)-dimensional potential-YTSF equation and a simplified model for reacting mixtures

In the paper, the generalized projective Riccati equation method is extended to construct some non-travelling wave solutions to a (3 + 1)-dimensional potential-YTSF equation and a simplified model for reacting mixtures. When some arbitrary functions included in these solutions are taken as some special functions, these solutions possess abundant structures.

New Exact Solutions and Conservation Laws to (3+1)-DimensionalPotential-YTSF Equation

Using the modified CK's direct method, we build therelationship between new solutions and old ones and find some new exactsolutions to the (3+1)-dimensional potential-YTSF equation. Based on theinvariant group theory, Lie point symmetry groups and Lie symmetries of the(3+1)-dimensional potential-YTSF equation are obtained. We also getconservation laws of the equation with the given Lie symmetry.

Generalized method to construct the solitonic solutions to [formula omitted]-dimensional nonlinear equation

A generalized method with computerized symbolic computation, which is called the generalized extended tanh-function method, is presented for the nonlinear equations of mathematical physics (NEMPs). Compared with most of the existing tanh-function method, the extended tanh-function method, the modified extended tanh-function method and generalized hyperbolic-function method, the proposed method is more powerful. By use of the method, we not only can successfully recover the previously known formal solutions but also construct new and more general formal solutions for some NEMPs. Make use of the method, we study the ( 3 + 1 ) -dimensional potential-YTSF equation and obtain rich new families of the exact solutions, including the nontraveling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions.

Generalized extended tanh-function method and its application

In this paper, a new generalized extended tanh-function method is presented for constructing soliton-like, period-form solutions of nonlinear evolution equations (NEEs). Compared with most of the existing tanh-function method, extended tanh-function method, the modified extended tanh-function method and generalized hyperbolic-function method, the proposed method is more powerful. By using this method, we not only can successfully recover the previously known formal solutions but also construct new and more general formal solutions for some NEEs. Make use of the method, we study the (3 + 1)-dimensional potential-YTSF equation and obtain rich new families of the exact solutions, including the non-travelling wave and coefficient functions’ soliton-like solutions, singular soliton-like solutions, periodic form solutions.

Bäcklund Transformation and Multiple Soliton Solutions for (3+1)-Dimensional Potential-YTSF Equation**The project supported by National Natural Science Foundation of China under Grant No. 10475056 and the President Foundation of the Chinese Academy of Sciences

We study an approach to constructing multiple soliton solutions of the (3+1)-dimensional nonlinear evolution equation. We take the (3+1)-dimensional potential-YTSF equation as an example. Using the extended homogeneous balance method, one can find a Backlund transformation to decompose the (3+1)-dimensional potential-YTSF equation into a set of partial differential equations. Starting from these partial differential equations, some multiple soliton solutions for the (3+1)-dimensional potential-YTSF equation are obtained by introducing a class of formal solutions.

New families of nontravelling wave solutions to a new (3+1)-dimensional potential-YTSF equation

Recently a new (3+1)-dimensional nonlinear evolution equation (called YTSF equation) was firstly presented by using the strong symmetry. In this Letter, the potential form of the YTSF equation is investigated. Auto-Backlund transformation is obtained, which and some ansatze are used to seek new types of exact solutions including some arbitrary functions. When these arbitrary functions are taken as some special functions, these solutions possess abundant structures. These solutions contain soliton-like solutions and rational solutions.