scholarly journals Solitary and self-similar solutions of two-component system of nonlinear Schrödinger equations

2006 ◽  
Vol 220 (2) ◽  
pp. 99-115 ◽  
Author(s):  
Tai-Chia Lin ◽  
Juncheng Wei
Keyword(s):  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Two Component System ◽  
Component System ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Two Component ◽  
Self Similar ◽  
Similar Solutions

scholarly journals Global Self-similar Solutions of a Class of Nonlinear Schrödinger Equations

2008 ◽  
Vol 2008 ◽  
pp. 1-9 ◽  
Author(s):  
Yaojun YE
Keyword(s):  
Nonlinear Term ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
The Cauchy Problem ◽  
Global Existence And Uniqueness ◽  
Self Similar ◽  
Similar Solutions

For a certain range of the valuepin the nonlinear term|u|pu, in this paper we mainly study the global existence and uniqueness of global self-similar solutions to the Cauchy problem for some nonlinear Schrödinger equations using the method of harmonic analysis.

scholarly journals Self-Similar Solutions for Nonlinear Schrödinger Equations

2009 ◽  
Vol 2009 ◽  
pp. 1-15 ◽  
Author(s):  
Yaojun Ye
Keyword(s):  
Mapping Method ◽  
Higher Order ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Small Data ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
Self Similar ◽  
Similar Solutions

We study the self-similar solutions for nonlinear Schrödinger type equations of higher order with nonlinear term|u|αuby a scaling technique and the contractive mapping method. For some admissible valueα, we establish the global well-posedness of the Cauchy problem for nonlinear Schrödinger equations of higher order in some nonstandard function spaces which contain many homogeneous functions. we do this by establishing some nonlinear estimates in the Lorentz spaces or Besov spaces. These new global solutions to nonlinear Schrödinger equations with small data admit a class of self-similar solutions.

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