Influence of small dispersion on self-focusing in spatially one-dimensional case

Abstract

The effect of the small dispersion on the self-focusing of solutions of the equations of nonlinear geometric optics in one-dimensional case is investigated. In the main order this influence is described by means of the universal special solution of the nonlinear Schrödinger equation, which is isomonodromic. Analytic and asymptotic properties of this solution are described.

arXiv commentin Russian

References in corpus (2)

• On Hamiltonian perturbations of hyperbolic systems of conservation laws, II: universality of critical behaviour
• Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painlevé Equation. I

Cited by in corpus (6)

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• Large-order asymptotics for multiple-pole solitons of the focusing nonlinear Schrödinger equation
• Broader Universality of Rogue Waves of Infinite Order
• Integrable Abel equation and asymptotics of symmetry solutions of Korteweg-de Vries equation
• Correlated many-body quantum dynamics of the Peregrine soliton
• Meromorphy of solutions for a wide class of ordinary differential equations of Painlevé type