Singular solutions of the L^2-supercritical biharmonic Nonlinear Schrodinger equation

TL;DR

This paper investigates singular solutions of the supercritical biharmonic nonlinear Schrödinger equation, revealing a universal self-similar profile and a quartic-root blowup rate through asymptotic analysis and simulations.

Contribution

It introduces a detailed analysis of peak-type singular solutions, identifying their universal profile and blowup rate in the supercritical regime.

Findings

Solutions exhibit a quartic-root blowup rate.

Collapse occurs with a quasi self-similar universal profile.

The profile is a zero-Hamiltonian solution of a nonlinear eigenvalue problem.

Abstract

We use asymptotic analysis and numerical simulations to study peak-type singular solutions of the supercritical biharmonic NLS. These solutions have a quartic-root blowup rate, and collapse with a quasi self-similar universal profile, which is a zero-Hamiltonian solution of a fourth-order nonlinear eigenvalue problem.