Propagation of infinitely narrow delta-solitons

TL;DR

This paper develops a framework for understanding the behavior of narrow delta-solitons in KdV equations as dispersion approaches zero, providing a new way to analyze soliton dynamics in this limit.

Contribution

It introduces a novel definition of weak solutions for KdV equations with small dispersion, enabling the derivation of a limit system describing soliton dynamics.

Findings

Defined weak solutions for KdV with small dispersion

Derived a limit system for zero dispersion soliton dynamics

Established a framework for analyzing delta-solitons in KdV

Abstract

We construct a definition of the weak solution to KdV type equations with small dispersion admitting the zero dispersion limit for soliton-like solutions. Using this definition, we obtain a system of equations (the limit problem as the dispersion tends to zero) that describes the soliton dynamics.