Ma Zheng-Yi

An extended Jacobian elliptic function method for the discrete mKdV lattice

In this paper, the discrete mKdV lattice is solved by using the modified Jacobian elliptic function expansion method. As a consequence, abundant families of Jacobian elliptic function solutions are obtained. When the modulus m→1, these periodic solutions degenerate to the corresponding solitary wave solutions, including bell-type and kink-type excitations.

The projective Riccati equation expansion method and variable separation solutions for the nonlinear physical differential equation in physics

Using the projective Riccati equation expansion (PREE) method, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with arbitrary functions for two nonlinear physical models are obtained. Based on one of the variable separation solutions and by choosing appropriate functions, new types of interactions between the multi-valued and single-valued solitons, such as a peakon-like semi-foldon and a peakon, a compacton-like semi-foldon and a compacton, are investigated.

Two classes of fractal structures for the (2+1)-dimensional dispersive long wave equation

Using the mapping approach via a Riccati equation, a series of variable separation excitations with three arbitrary functions for the (2+1)-dimensional dispersive long wave (DLW) equation are derived. In addition to the usual localized coherent soliton excitations like dromions, rings, peakons and compactions, etc, some new types of excitations that possess fractal behaviour are obtained by introducing appropriate lower-dimensional localized patterns and Jacobian elliptic functions.

General Jacobian elliptic function expansion method and its applications

An extended Jacobian elliptic function expansion method is presented and successfully applied to the nonlinear Schrodinger (NLS) equation and Zakharov equation. We obtain some new solutions besides Fu et als results. The results show that our method is more powerful to construct Jacobian elliptic function and can be applied to other nonlinear physics systems.

New Exact Solutions to （2＋1）-Dimensional Variable Coefficients Broer-Kaup Equations

In this paper, using the variable coefficient generalized projected Ricatti equation expansion method, we present explicit solutions of the (2+1)-dimensional variable coefficients Broer–Kaup (VCBK) equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.

Fission and Fusion of Localized Coherent Structures for a Higher-Order Broer Kaup System

Starting from a Backlund transformation and taking a special ansatz for the function f, we can obtain a much more general expression of solution that includes some variable separated functions for the higher-order Broer–Kaup system. From this expression, we investigate the interactions of localized coherent structures such as the multi-solitonic excitations and find the novel phenomenon that their interactions have non-elastic behavior because the fission/fusion may occur after the interaction of each localized coherent structure.

Doubly Periodic Propagating Wave Patterns of (2+1)-Dimensional Maccari System

Using the variable separation approach, we obtain a general exact solution with arbitrary variable separation functions for the (2+1)-dimensional Maccari system. By introducing Jacobi elliptic functions dn and nd in the seed solution, two types of doubly periodic propagating wave patterns are derived. We investigate the wave patterns evolution along with the modulus k increasing, many important and interesting properties are revealed.

Interaction between two folded solitary waves for a modified Broer–Kaup system

By means of a Painleve–Backlund transformation and a multi-linear separation-of-variable approach, abundant localized coherent excitations of a modified Broer–Kaup system are derived. There appear possible phase shifts for the interactions of the (2+1)-dimensional novel localized structures, which are discussed in this paper.

New Fractal Localized Structures in Boiti-Leon-Pempinelli System

A novel phenomenon that the localized coherent structures of a (2+1)-dimensional physical model possess fractal behaviors is revealed. To clarify the interesting phenomenon, we take the (2+1)-dimensional Boiti–Leon–Pempinelli system as a concrete example. Starting from an extended homogeneous balance approach, a general solution of the system is derived. From which some special localized excitations with fractal behaviors are obtained by introducing some types of lower-dimensional fractal patterns.

Variable Separated Solutions and Four-Dromion Excitations for (2+1)-Dimensional Nizhnik–Novikov–Veselov Equation

Using the mapping approach via the projective Riccati equations, several types of variable separated solutions of the (2+1)-dimensional Nizhnik–Novikov–Veselov equation are obtained, including multiple-soliton solutions, periodic-soliton solutions, and Weierstrass function solutions. Based on a periodic-soliton solution, a new type of localized excitation, i.e., the four-dromion soliton, is constructed and some evolutional properties of this localized structure are briefly discussed.