Chunli Chen

Localized solutions with chaotic and fractal behaviours in a (2+1)-dimensional dispersive long-wave system

A substrate serving as a heat sink for a semiconductor efficiently radiates heat from a semiconductor element mounted thereon. The substrate consists of a composite alloy metal which consists of a sintered body of a metal powder having a high melting point such as W and Mo impregnated with a filling metal such as Cu and Ag, wherein the sintered body of a metal powder having a high melting point has a grain size composition of a combination of a plurality of powder groups having statistically different average grain sizes from group to group, and the powder of each group is dispersed uniformly.

(2+1)-dimensional (M+N)-component AKNS system: Painlevé integrability, infinitely many symmetries, similarity reductions and exact solutions

The (2+1)-dimensional (M+N)-component AKNS system that is derived from the inner parameter dependent symmetry constraint of the KP equation is studied in detail. First, the Painleve integrability of the model is proved by using the standard WTC and Kruskal approach. Using the formal series symmetry approach, the generalized KMV symmetry algebra and the related symmetry group are found. The two-dimensional similarity partial differential equation reductions and the ordinary differential equation reductions are obtained from the generalized KMV symmetry algebra and the direct method. Abundant localized coherent structures are revealed by the variable separation approach. Some special types of the localized excitations like the multiple solitoffs, dromions, lumps, ring solitons, breathers and instantons are plotted also.

Soliton excitations and periodic waves without dispersion relation in shallow water system

Abstract Using the nonstandard and standard truncations of a modified Conte’s invariant Painleve expansion for the dispersive long wave equation system, two types of soliton excitations without any dispersive relations are found. Four types of periodic waves expressed by Jacobi elliptic functions are found by the truncations of a special extended Painleve expansion. The soliton solutions are special cases of the corresponding two of the given periodic solutions. The dispersion relations of the solutions are crucially dependent on the boundary conditions.

Lie symmetry analysis and some new exact solutions of the Wu–Zhang equation

The Lie symmetry analysis and the basic similarity reductions are performed for the Wu–Zhang equation, a 2+1 dimensional nonlinear dispersive wave equation. Some new exact solutions generated from the similarity transformation are provided. They demonstrate some new three-dimensional features of a single solitary wave and two interacting solitary waves.

On Boussinesq models of constant depth

The mathematical properties, such as integrability, symmetries and multiple solitary wave solutions of Boussinesq models of constant depth are studied. An integrable modified Boussinesq model has been identified.

Solitary wave solutions for a general Boussinesq type fluid model

Abstract The possible solitary wave solutions for a general Boussinesq (GBQ) type fluid model are studied analytically. After proving the non-Painleve integrability of the model, the first type of exact explicit travelling solitary wave with a special velocity selection is found by the truncated Painleve expansion. The general solitary waves with different travelling velocities can be studied by casting the problems to the Newtonian quasi-particles moving in some proper one dimensional potential fields. For some special velocity selections, the solitary waves possess different shapes, say, the left moving solitary waves may possess different shapes and/or amplitudes with those of the right moving solitons. For some other velocities, the solitary waves are completely prohibited. There are three types of GBQ systems (GBQSs) according to the different selections of the model parameters. For the first type of GBQS, both the faster moving and lower moving solitary waves allowed but the solitary waves with“middle” velocities are prohibit. For the second type of GBQS all the slower moving solitary waves are completely prohibit while for the third type of GBQS only the slower moving solitary waves are allowed. Only the solitary waves with the almost unit velocities meet the weak non-linearity conditions.

The motion of surfaces in geodesic coordinates and 2+1-dimensional breaking soliton equation

The system of evolution equations for general motion of surfaces in geodesic coordinates is analyzed to reduce the number of variables as well as equations. A special choice for some variants deduces that the surface and the motion of surface correspond to a nonlinear Schrodinger equation and a 2+1-dimensional breaking soliton equation; respectively. We also study some geometric properties corresponding to the integrals of the motion of surface and the motion of the curve on the surface. The spectral parameter is introduced.

On Head-on Collisions between Two Solitary Waves of Nwogu's Boussinesq Model

In this paper, we consider the head-on collision between two solitary waves of Nwogus Boussinesq equation which contains one parameter c that is related to that the horizontal velocities at what level are chosen as the horizontal velocity variables. We apply the perturbation method to derive an approximate solution to this equation and investigate the mechanics of the head-on collision. The impacts of the parameter c on the phase shifts and the maximum run-up amplitude of two colliding waves are studied. Comparison between our results and that of the integrable classical Boussinesq equation is also given.

The Lund–Regge surface and its motion’s evolution equation

The system of evolution equations for general motion of surfaces in orthogonal coordinates is analyzed to reduce the number of variables as well as equations. The explicit expression of the Lund–Regge surface is obtained. When the surface corresponds to the Lund–Regge equation, we prove that some components of velocity satisfy the linearizations of the Lund–Regge equation. The soliton solution is derived and one special case of the Lund–Regge surface is studied.