Nonlinear Profile Decomposition and the Concentration Phenomenon for Supercritical Generalized KdV Equations

TL;DR

This paper develops a nonlinear profile decomposition for supercritical generalized KdV equations, leading to a concentration result for finite time blow-up solutions of Type II, advancing understanding of solution behavior in critical regimes.

Contribution

It introduces a novel nonlinear profile decomposition technique for supercritical gKdV equations and derives a concentration phenomenon for Type II blow-up solutions.

Findings

Established nonlinear profile decomposition for supercritical gKdV solutions

Proved concentration of solutions at blow-up time for Type II solutions

Enhanced understanding of solution dynamics near singularities

Abstract

A nonlinear profile decomposition is established for solutions of supercritical generalized Korteweg-de Vries equations. As a consequence, we obtain a concentration result for finite time blow-up solutions that are of Type II.