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

Victor M. Perez-Garcia

doi:10.1016/j.physd.2003.12.010

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arXiv · nlin/0312007

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

Victor M. Perez-Garcia

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Abstract

In this paper we study the phase of self-similar solutions to general Nonlinear Schrödinger 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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Victor M. Perez-Garcia. 2003-12-03. Self-similar solutions and collective coordinate methods for Nonlinear Schrodinger Equations. https://doi.org/10.1016/j.physd.2003.12.010

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