Yan Zhen-Ya

New Jacobian Elliptic Function Solutions to Modified KdV Equation: I

Recently, we obtained thirteen families of Jacobian elliptic function solutions of mKdV equation by using our extended Jacobian elliptic function expansion method. In this note, the mKdV equation is investigated and another three families of new doubly periodic solutions (Jacobian elliptic function solutions) are found again by using a new transformation, which and our extended Jacobian elliptic function expansion method form a new method still called the extended Jacobian elliptic function expansion method. The new method can be more powerful to be applied to other nonlinear differential equations.

New Similarity Reductions and Compacton Solutions for Boussinesq-Like Equations with Fully Nonlinear Dispersion

In this paper, similarity reductions of Boussinesq-like equations with nonlinear dispersion (simply called equations) , which is a generalized model of Boussinesq equation and modified Bousinesq equation , are considered by using the direct reduction method. As a result, several new types of similarity reductions are found. Based on the reduction equations and some simple transformations, we obtain the solitary wave solutions and compacton solutions (which are solitary waves with the property that after colliding with other compacton solutions, they re-emerge with the same coherent shape) of equations and equations, respectively.

New Explicit Solitary Wave Solutions and Periodic Wave Solutions for the Generalized Coupled Hirota Satsuma KdV System

In this paper, we study the generalized coupled Hirota-Satsuma KdV system by using the new generalized transformation in homogeneous balance method. As a result, many explicit exact solutions, which contain new solitary wave solutions, periodic wave solutions, and the combined formal solitary wave solutions, and periodic wave solutions, are obtained

Abundant Symmetries and Exact Compacton—Like Structures in the Two—Parameter Family of the Estevez—Mansfield—Clarkson Equations

The two-parameter family of Estevez–Mansfield–Clarkson equations with fully nonlinear dispersion (called E(m,n) equations), which is a generalized model of the integrable Estevez–Mansfield–Clarkson equation , is presented. Five types of symmetries of the E(m,n) equation are obtained by making use of the direct reduction method. Using these obtained reductions and some simple transformations, we obtain the solitary-like wave solutions of equation. In addition, we also find the compacton solutions (which are solitary waves with the property that after colliding with other compacton solutions, they reemerge with the same coherent shape) of E(3, 2) equation and for its potentials, say, , and compacton-like solutions of equations, respectively. Whether there exist compacton-like solutions of the other E(m,n) equation with is still an open problem.

New explicit exact solutions for a generalized Hirota-Satsuma coupled KdV system and a coupled MKdV equation

In this paper, we make use of a new generalized ansatz in the homogeneous balance method, the well-known Riccati equation and the symbolic computation to study a generalized Hirota-Satsuma coupled KdV system and a coupled MKdV equation, respectively. As a result, numerous explicit exact solutions, comprising new solitary wave solutions, periodic wave solutions and the combined formal solitary wave solutions and periodic wave solutions, are obtained.

On a new algorithm of constructing solitary wave solutions for systems of nonlinear evolution equations in mathematical physics

According to the improved sine-cosine method and Wu-elimination method, a new algorithm to construct solitary wave solutions for systems of nonlinear evolution equations is put forward. The algorithm has some conclusions which are better than what the hyperbolic function method known does and simpler in use. With the aid of MATHEMATICA, the algorithm can be carried out in computer.

New Symmetry Reductions, Dromions-Like and Compacton Solutions for a 2D BS(m,n) Equations Hierarchy with Fully Nonlinear Dispersion*

We have found two types of important exact solutions, compacton solutions, which are solitary waves with the property that after colliding with their own kind, they re-emerge with the same coherent shape very much as the solitons do during a completely elastic interaction, in the and even models, and dromion solutions (exponentially decaying solutions in all direction) in many and models. In this paper, symmetry reductions in are considered for the break soliton-type equation with fully nonlinear dispersion (called equation) , which is a generalized model of break soliton equation , by using the extended direct reduction method. As a result, six types of symmetry reductions are obtained. Starting from the reduction equations and some simple transformations, we obtain the solitary wave solutions of equations, compacton solutions of equations and the compacton-like solution of the potential form (called ) . In addition, we show that the variable admits dromion solutions rather than the field itself in equation.

New Soliton Solutions with Compact Support for a Family of Two-Parameter Regularized Long-Wave Boussinesq Equations*

Searching for special solitary wave solutions with compact support is of important significance in soliton theory. In this paper, to understand the role of nonlinear dispersion in pattern formation, a family of the regularized long-wave Boussinesq equations with fully nonlinear dispersion (simply called equations), ( const.), is studied. New solitary wave solutions with compact support of equations are found. In addition we find another compacton solutions of the two special cases, equation and equation. It is found that the nonlinear dispersion term in a nonlinear evolution equation is not a necessary condition of that it possesses compacton solutions.

Symmetry Reductions, Integrability and Solitary Wave Solutions to High-Order Modified Boussinesq Equations with Damping Term*

Both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou are extended to reduce the high-order modified Boussinesq equation with the damping term (HMBEDT) arising in the general Fermi–Pasta–Ulam model. As a result, several types of similarity reductions are obtained. It is easy to show that the nonlinear wave equation is not integrable under the sense of Ablowitzs conjecture from the reduction results obtained. In addition, kink-shaped solitary wave solutions, which are of important physical significance, are found for HMBEDT based on the obtained reduction equation.

Similarity Reduction and Integrability for the Nonlinear Wave Equations from EPM Model

Four types of similarity reductions are obtained for the nonlinear wave equation arising in the elasto-plastic-microstructure model by using both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou. As a result, the nonlinear wave equation is not integrable.