Self-similar solutions of NLS-type dynamical systems

Details Self-similar solutions of NLS-type dynamical systems Self-similar solutions of NLS-type dynamical systems

1999-09-21

arxiv.org/abs/solv-int/9909021v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

18 pages, AmsTeX

Scientific paper

We study self-similar solutions of NLS-type dynamical systems. Lagrangian approach is used to show that they can be reduced to three canonical forms, which are related by Miura transformations. The fourth Painleve equation (PIV) is central in our consideration - it connects Heisenberg model, Volterra model and Toda model to each other. The connection between the rational solutions of PIV and Coulomb gas in a parabolic potential is established. We discuss also the possibility to obtain an exact solution for optical soliton i.e. of the NLS equation with time-dependent dispersion.

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