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

## TL;DR

This paper investigates how small dispersion affects self-focusing in one-dimensional nonlinear geometric optics, using a universal solution of the nonlinear Schrödinger equation to describe the influence.

## Contribution

It introduces a universal isomonodromic solution of the nonlinear Schrödinger equation to analyze small dispersion effects on self-focusing.

## Key findings

- Small dispersion influences self-focusing behavior in nonlinear optics.
- The universal solution provides a detailed description of the effect.
- Analytic and asymptotic properties of the solution are characterized.

## 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 Schr\"odinger equation, which is isomonodromic. Analytic and asymptotic properties of this solution are described.