Local well-posedness for a quasilinear Schr "odinger equation with\n degenerate dispersion

2020/04/08 by Benjamin Harrop‐Griffiths, Harrop-Griffiths, Benjamin, Jeremy L. Marzuola +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2004.04134

openalex publication_date 2020/04/08 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We consider a quasilinear Schr "odinger equation on mathbb R for which the\ndispersive effects degenerate when the solution vanishes. We first prove local\nwell-posedness for sufficiently smooth, spatially localized, degenerate initial\ndata. As a corollary in the focusing case we obtain a short time stability\nresult for the energy-minimizing compact breather.\n

Citations

• Orbital stability of standing waves for some nonlinear Schr�dinger equations
• Gevrey class regularity for the solutions of the Navier-Stokes equations

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