Compactons and their variational properties for degenerate kdv and nls in dimension 1

Pierre Germain, Benjamin Harrop-Griffiths, Jeremy L. Marzuola

Research output: Contribution to journalArticle

Abstract

We analyze the stationary and traveling wave solutions to a family of degenerate dispersive equations of KdV-and NLS-type. In stark contrast to the standard soliton solutions for nondegenerate KdV and NLS equations, the degeneracy of the elliptic operators studied here allows for compactly supported steady or traveling states. As we work in 1 dimension, ODE methods apply; however, the models considered have formally conserved Hamiltonian, Mass, and Momentum functionals, which allow for variational analysis as well.

Original languageEnglish (US)
Article number1538
Pages (from-to)1-32
Number of pages32
JournalQuarterly of Applied Mathematics
Volume78
DOIs
StatePublished - 2020

ASJC Scopus subject areas

  • Applied Mathematics

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