Variational Approach to Complicated Similarity Solutions of Higher-Order Nonlinear PDEs. II

TL;DR

This paper investigates complex similarity solutions of higher-order nonlinear PDEs, revealing their blow-up, extinction, and traveling wave behaviors through variational methods that identify countable families of solutions.

Contribution

It introduces a variational framework to find and analyze complex similarity solutions of higher-order nonlinear PDEs, including blow-up and traveling wave solutions.

Findings

Existence of various blow-up and extinction solutions.

Identification of traveling wave solutions.

Countable families of compactly supported solutions.

Abstract

Some higher-order quasilinear parabolic, hyperbolic, and nonlinear dispersion equations are shown to admit various blow-up, extinction, and travelling wave solutions, which reduce to variational problems admitting countable families of compactly supported solutions.