The Davey-Stewartson equation set is reduced to Lienerd equation first,and then the explicit and exact solutions for these equations,which include exact isolated wave solutions,periodic solutions and exact isolated-type wave solutions,are obtained through solving the Lienard equation.
If Msm(c) is minimal, we prove that Msm must be flat with index s in a (2m-1)-pseudo-sphere with the same index. We also use techniques from soliton theory to get the correspondence between a kind of flat m-dimensional submanifolds with index s in the (2m-1)-dimensional pseudo-sphere Ns2m-1 and the system I.
Chapter 1 of this dissertation is devoted to introducing the history and development of the soliton theory, the ideas of mathematics mechanization and computer algebra, and some methods seeking exact solutions for the nonlinear evolution equation, such as inverse scattering method, symmetry reduction method, Backlund transformation, Darboux transformation , Hirota bilinear method, Painleve analysis method, AC = BD model, and so on.
This is done by using a travelling wave method to formulate one-soliton solution and the finite difference method to the numerical solutions and the interactions between the solitons for the generalized nonlinear Schrodinger equations.
This achieved using a traveling wave method to formulate one-soliton solution and the P-R method is employed to the numerical solutions and the interactions between the solitons for the generalized nonlinear systems in 2-space.
Parameter region for existence of solitons in generalized KdV equation
This paper considers the generalized KdV equation with or without natural boundary conditions and provides a parameter region for solitons and solitary waves, and also modifies a result of Zabusky's.
Solitons in relativistic laser-plasma interactions
It is derived studying the dissemination of magnet sound wave in cold plasma, the isolated wave in transmission line, and the isolated wave in the boundary surface of the divided layer fluid.
In the absence of a simple method of the evaluation of wave component interactions, investigations of the wave development must be based on the entire wave system, and cannot be applied to isolated wave components.
Extrapolation to the ideal case of a single isolated wave gives Vmax proportional to size.
An estimate can be made for the conditions under which the isolated wave train is observed above the ever present background.
A Numerical Method for Constructing a Self-Similar Isolated Wave Solution
An investigation is made of the behavior of the nth harmonic of the periodic solution of the Korteweg-de Vries equation as a function of the index n in the intermediate region which is not usually investigated by soliton theory.
Soliton theory for the weakly incommensurate phase of monolayer krypton or graphite
Application of Soliton Theory to the Construction of Isometric Immersions of Mn1(c1) ×Mn2(c2) into Constant Curvature Spaces Mn(
In this paper, we apply the soliton theory to the case of isometric immersion in differential geometry and obtain a family of isometric immersions from Mn1(c1) ×Mn2(c2) to space forms Mn(c) by introducing 2-parameter loop algebra.
Application of Soliton Theory to the Construction of Isometric Immersions of $$