Dai Zheng-de

Exact Periodic Solitary-Wave Solution for KdV Equation

A new technique, the extended homoclinic test technique, is proposed to seek periodic solitary wave solutions of integrable systems. Exact periodic solitary-wave solutions for classical KdV equation are obtained using this technique. This result shows that it is entirely possible for the (1+1)-dimensional integrable equation that there exists a periodic solitary-wave.

New Exact Periodic Solitary-Wave Solutions for New (2+1)-Dimensional KdV Equation

The extended homoclinic test function method is a kind of classic, efficient and well-developed method to solve nonlinear evolution equations. In this paper, with the help of this approach, we obtain new exact solutions (including kinky periodic solitary-wave solutions, periodic soliton solutions, and cross kink-wave solutions) for the new (2+1)-dimensional KdV equation. These results enrich the variety of the dynamics of higher-dimensional nonlinear wave field.

Periodic Bifurcation and Soliton Deflexion for Kadomtsev–Petviashvili Equation

The spatial–temporal bifurcation for Kadomtsev–Petviashvili (KP) equations is considered. Exact two-soliton solution and doubly periodic solution to the KP-I equation, and two classes of periodic soliton solutions in different directions to KP-II are obtained using the bilinear form, homoclinic test technique and temporal and spatial transformation method, respectively. The equilibrium solution u0 = −(1/6), a unique spatial–temporal bifurcation which is periodic bifurcation for KP-I and deflexion of soliton for KP-II, is investigated.

Homoclinic Bifurcation for Boussinesq Equation with Even Constraint

The exact homoclinic orbits and periodic soliton solution for the Boussinesq equation are shown. The equilibrium solution u0 = −1/6 is a unique bifurcation point. The homoclinic orbits and solitons will be interchanged with the solution varying from one side of -1/6 to the other side. The solution structure may be understood preliminary.

Homoclinic Breather-Wave with Convective Effect for the (1+1)-Dimensional Boussinesq Equation

A new type of two-wave solution, i.e. a homoclinic breather-wave solution with convective effect, for the (1+1)-dimensional Boussinesq equation is obtained using the extended homoclinic test method. Moreover, the mechanical feature of the wave solution is investigated and the phenomenon of homoclinic convection of the two-wave is exhibited on both sides of the equilibrium. These results enrich the dynamical behavior of (1+1)-dimensional nonlinear wave fields.

Inertial fractal sets for dissipative Zakharov system

Abstract[1] has proved that the dissipative Zakharov system has anε2-weak compact attractor. In this paper, we further show that the dissipative Langmuir waves in plasmas admit an inertial fractal set of (ε2,ε1)-type. We also make the estimates on its fractal dimension and exponential attraction.

New Rogue Wave Solutions of (1+2)-Dimensional Non-Isospectral KP-II Equation

The generalized binary Darboux transformation for the (1+2)-dimensional non-isospectral KP-II equation is presented. Moreover, as a direct application, the new rogue wave solutions for the (1+2)-dimensional non-isospectral KP-II equation are constructed by the generalized binary Darboux transformation.

Heteroclinic Breather-Wave Solutions for Davey–Stewartson Equation

Exact heteroclinic breather-wave solutions for Davey–Stewartson (DSI, DSII) system with periodic boundary condition are constructed using Hirotas bilinear form method and generalized ansatz method. The heteroclinic structure of wave is investigated.

New Mechanical Feature of Two-Solitary Wave to the KdV Equation

New breather solitary solution and two-solitary solutions depending on constant equilibrium solution to the Korteweg de Vries equation are obtained by using an extended homoclinic test approach. A new mechanical feature of a two-solitary wave, namely, dependence of propagation direction and shape on position of equilibrium point, is investigated.

Periodic Homoclinic Wave of (1+1)-Dimensional Long--Short Wave Equation

The exact periodic homoclinic wave of (1+1)D long-short wave equation is obtained using an extended homoclinic test technique. This result shows complexity and variety of dynamical behaviour for a (1+1)-dimensional long-short wave equation.