Self-similar solutions and collective coordinate methods for Nonlinear Schrodinger Equations

Details Self-similar solutions and collective coordinate methods for Nonlinear Schrodinger Equations Self-similar solutions and collective coordinate methods for Nonlinear Schrodinger Equations

2003-12-03

arxiv.org/abs/nlin/0312007v1

Nonlinear Sciences

Pattern Formation and Solitons

Scientific paper

10.1016/j.physd.2003.12.010

In this paper we study the phase of self-similar solutions to general Nonlinear Schr\"odinger equations. From this analysis we gain insight on the dynamics of nontrivial solutions and a deeper understanding of the way collective coordinate methods work. We also find general evolution equations for the most relevant dynamical parameter $w(t)$ corresponding to the width of the solution. These equations are exact for self-similar solutions and provide a shortcut to find approximate evolution equations for the width of non-self-similar solutions similar to those of collective coordinate methods.

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