Dimensional Dispersive Long Wave Equation Research Articles

A new general algebraic method with symbolic computation to construct new travelling wave solution for the (1 + 1)-dimensional dispersive long wave equation

With the aid of symbolic computation, a new algebraic method, named Riccati equation rational expansion (RERE) method, is devised for constructing multiple travelling wave solutions for nonlinear evolution equations (NEEs). Compared with most existing tanh methods for finding travelling wave solutions, the proposed method not only recover the results by most known algebraic methods, but also provides new and more general solutions. With the aid of symbolic computation, we choose (1 + 1)-dimensional dispersive long wave equation (DLWE) to illustrate our method. As a result, we obtain many types of solutions including rational form solitary wave solutions, triangular periodic wave solutions and rational wave solutions. The properties of the new solitary wave solutions are shown by some figures.

Symbolic computation and construction of soliton-like solutions to the (2 + 1)-dimensional dispersive long-wave equations

By means of a new Riccati equation expansion method, we consider the (2 + 1)-dimensional dispersive long-wave equations u yt+η xx+ 1 2 (u 2) xy=0 , η t +( uη+ u+ u xy ) x =0. As a result, we not only can successfully recover the previously known formal solutions obtained by known tanh function methods but also construct new and more general formal solutions. The solutions obtained include the nontravelling wave and coefficient functions’ soliton-like solutions, singular soliton-like solutions, triangular functions solutions.

Multisoliton-like solutions for (2+1)-dimensional dispersive long wave equations and (2+1)-dimensional Broer-Kaup equations

By extending homogeneous balance method and improving some of its procedures, we have obtained new multi-soliton-like solutions for (2+1)-dimensional dispersive long-wave equations and (2+1)-dimensional Broer-Kaup equations- The solution we obtained presents generality, because it contain some multisoliton-like solutio ns which are given in other papers-

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

It is known that in high dimensions there exist abundant localized excitations such as dromions, lumps, ring soliton solutions and so on. In this paper, the possible chaotic and fractal localized structures are revealed for the (2+1)-dimensional dispersive long-wave equation. The chaotic and fractal dromion and lump patterns of the model are constructed by some types of lower-dimensional chaotic and fractal patterns.

New multi-soliton solutions and travelling wave solutions of the dispersive long-wave equations

Using the extended homogeneous balance method, the (1+1)-dimensional dispersive long-wave equations have been solved. Starting from the homogeneous balance method, we have obtained a nonlinear transformation for simplifying a dispersive long-wave equation into a linear partial differential equation. Usually, we can obtain only a type of soliton-like solution. In this paper, we have further found some new multi-soliton solutions and exact travelling solutions of the dispersive long-wave equations from the linear partial equation.

Abundant coherent structures of the dispersive long-wave equation in (2+1)-dimensional spaces

By means of the variable separation approach, the abundant localized coherent structures of a (2+1)-dimensional dispersive long-wave equation (2DDLWE) are given out. The result formula for the coherent solutions is totally the same as that of the asymmetric Nizhnik–Novikov–Veselov equation and the asymmetric Davey–Stewartson equation. Especially, from the figure plots of three-soliton solution, we find that the interaction among the travelling saddle type ring solitons is elastic.

Exotic Localized Coherent Structures of the (2+1)-Dimensional Dispersive Long-Wave Equation

This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structures in the (2+1)-dimensional dispersive long-wave equations . Starting from the homogeneous balance method, we find that the richness of the localized coherent structures of the model is caused by the entrance of two variable-separated arbitrary functions. For some special selections of the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, breathers, instantons and ring solitons.

Multiple Soliton-like and Periodic-like Solutions to the Generalization of Integrable (2+1)-Dimensional Dispersive Long-Wave Equations

In this paper, the generalization of integrable (2+1)-dimensional dispersive long-wave equations (GIDLWE) introduced by Boiti et al. is investigated. The idea of the homogeneous balance method, whi...

Multiple Soliton Solutions of the Dispersive Long-Wave Equations

Using a simple homogeneous balance method, which is very concise and primary, we find the multiple soliton solutions of the dispersive long-wave equations. The method can be generalized to deal with the higher dimensional dispersive long-wave equations and other class of nonlinear equation.

Multiple Soliton-Like Solutions for (2 + 1)-Dimensional Dispersive Long-Wave Equations

By using a homogeneous balance method,multiple-solitonlike solutions of the (2 +1)-dimensional dispersive long-wave equation areconstructed. The method used here can be generalized toa wide class of nonlinear evolution equations.

Dromion solutions for dispersive long-wave equations in two space dimensions

By using the homogeneous balance method, we show that the dromion solutions exist for the (2+1)-dimensional dispersive long-wave equations. It is conjectured that the method used here can be generalized to a class of nonlinear evolution equation. The method here is very concise and primary.

The Generalisation of Integrable (2+1)-Dimensional Dispersive Long-Wave Equations

In this paper, the generalisation of integrable (2+1)-dimensional dispersive long-wave equation (GDLWE) introduced by Boiti et al. is considered and is shown to possess the Painleve (P-) property. The bilinear transformation is obtained straightforwardly from the Painleve analysis.