Dispersive Long Wave Equation Research Articles

New Exact Solutions to Dispersive Long-Wave Equations in(2+1)-Dimensional Space

New exact solutions expressed by the Jacobi ellipticfunctions are obtained to the (2+1)-dimensional dispersive long-waveequations by using the modified F-expansion method. In the limit case, newsolitary wave solutions and triangular periodic wave solutions are obtainedas well.

New Complexiton Solutions of (1+1)-Dimensional Dispersive LongWave Equation

By means of two different Riccatiequations with different parameters as subequation in thecomponents of finite rational expansion method, new complexitonsolutions for the (1+1)-dimensional dispersive long wave equationare successfully constructed, which include various combination oftrigonometric periodic and hyperbolic function solutions, variouscombination of trigonometric periodic and rational functionsolutions, and various combination of hyperbolic and rationalfunction solutions.

New type of exact solitary wave solutions for dispersive long-wave equation and Benjamin equation

On the basis of homogeneous balance method, tanh-function method and auxiliary equation method, new types of exact solitary wave solutions of the dispersive long-wave equation and Benjamin equation are constructed by using a new auxiliary equation and with the aid of computer algebraic system Mathematica in this paper. This method also can be used to find new solitary wave solutions of other nonlinear evolution equations.

Symbolic computation and new families of exact solutions to the (2+1)-dimensional dispersive long-wave equations

Abstract In this Letter, We present a further generalized algebraic method to the (2 + 1)-dimensional dispersive long-wave equations (DLWS), As a result, we can obtain abundant new formal exact solutions of the equation. The method can also be applied to solve more (2 + 1)-dimensional (or (3 + 1)-dimensional) nonlinear partial differential equations (NPDEs).

Periodic Wave Solutions to Dispersive Long-Wave Equations in(2+1)-Dimensional Space**The project supported by the Natural Science Foundationof Shandong Province of China under Grant No. 2004zx16

Periodic wave solutions to the dispersive long-waveequations are obtained by using the F-expansion method, which can be thoughtof as a generalization of the Jacobi elliptic function method. In the limitcase, solitary wave solutions are obtained as well.

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.

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.

Some New Exact Solutions to the Dispersive Long-Wave Equation in (2+1)-Dimensional Spaces**The project supported by National Key Basic Research Development Program of China under Grant No. 1998030600 and National Natural Science Foundation of China under Grant No. 10072013

In this paper, by using a further extended tanh method and symbolic computation system, some new soliton-like and period form solutions of the dispersive long-wave equation in (2+1)-dimensional spaces are obtained.

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.

Group theoretical analysis of dispersive long wave equations in two space dimensions

The symmetry algebra of an integrable dispersive long-wave equation in two space dimensions is shown to be infinite-dimensional and to have a Kac-Moody-Virasoro structure. The corresponding symmetry group is used to generate a large number of new solutions, in particular solitons, kinks and periodic waves. These waves have wave crests of quite general shapes. The results are compared to those for a nonintegrable two-space-dimensional dispersive long-wave equation, for which the symmetry group is finite-dimensional and wave crests are always straight lines.

Integrable two-dimensional generalisation of the sine- and sinh-Gordon equations

A two-dimensional generalisation of the sine- and the sinh-Gordon equations, which one refers to as the shine-Gordon equations, is obtained and solved through the inverse spectral transform (IST) method. The Backlund transformation and nonlinear superposition formula are constructed and explicit wave solitons are given. It is shown also that a slightly different procedure furnishes an IST-solvable extension in 2+1 dimensions of the dispersive long-wave equation.