Self - Similar Solutions for Nonlinear Schrodinger Equations ∗
نویسندگان
چکیده
In this paper we study self-similar solutions for nonlinear Schrödinger equations using a scaling technique and the partly contractive mapping method. We establish the small global well-posedness of the Cauchy problem for nonlinear Schrödinger equations in some non-reflexive Banach spaces which contain many homogeneous functions. This we do by establishing some a priori nonlinear estimates in Besov spaces, employing the mean difference characterization and multiplication in Besov spaces. These new global solutions to nonlinear Schrödinger equations with small data admit a class of self-similar solutions. Our results improve and extend the well-known results of Planchon [18], Cazenave and Weissler [4, 5] and Ribaud and Youssfi [20].
منابع مشابه
Solutions structure of integrable families of Riccati equations and their applications to the perturbed nonlinear fractional Schrodinger equation
Some preliminaries about the integrable families of Riccati equations and solutions structure of these equations in several cases are presented in this paper, then by using of definitions for fractional derivative we apply the new extended of tanh method to the perturbed nonlinear fractional Schrodinger equation with the kerr law nonlinearity. Finally by using of this method and solutions of Ri...
متن کاملSolution and stability analysis of coupled nonlinear Schrodinger equations
We consider a new type of integrable coupled nonlinear Schrodinger (CNLS)equations proposed by our self [submitted to Phys. Plasmas (2011)]. The explicitform of soliton solutions are derived using the Hirota's bilinear method.We show that the parameters in the CNLS equations only determine the regionsfor the existence of bright and dark soliton solutions. Finally, throughthe linear stability an...
متن کاملرفتار سالیتونی در مدلهای ناپایدار باروکیلینیک
Here we concern ouraelves with the derivation of a system of evolution equations for slowly varying amplitude of a baroclinic wave packet. The self-induced transparency, Sine-Gordon, and nonlinear Schrodinger equations, all of which possess soliton solutions, each arise for different inviscid limits. The presence of viscosity, however, alters the form of the evolution equations and changes th...
متن کاملOn the split-step method for the solution of nonlinear Schr"{o}dinger equation with the Riesz space fractional derivative
The aim of this paper is to extend the split-step idea for the solution of fractional partial differential equations. We consider the multidimensional nonlinear Schr"{o}dinger equation with the Riesz space fractional derivative and propose an efficient numerical algorithm to obtain it's approximate solutions. To this end, we first discretize the Riesz fractional derivative then apply the Crank-...
متن کاملTopological and Non-Topological Soliton Solutions of the Coupled Klein-Gordon-Schrodinger and the Coupled Quadratic Nonlinear Equations
In this paper, two solitary wave solutions are obtained for the Coupled Klein-Gordon-Schrodinger and Coupled quadratic nonlinear equations by the ansatz method. Both topological and non-topological solitary wave solutions are obtained.
متن کامل