Small-amplitude self-similar solutions for one-dimensional nonlinear dispersive equations
Abstract
Given a nonlinear dispersive equation which admits a scaling invariance, there may exist self-similar solutions. In this work, we present a systematic approach for the construction of small-amplitude self-similar solutions, together with precise asymptotic descriptions at both small and large frequency scales. These ideas are then applied to three classic dispersive models: the modified Benjamin-Ono, the quartic Korteweg-de Vries and the cubic nonlinear Schr\"odinger equations.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.