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 language | English (US) |
|---|---|
| Article number | 1538 |
| Pages (from-to) | 1-32 |
| Number of pages | 32 |
| Journal | Quarterly of Applied Mathematics |
| Volume | 78 |
| DOIs | |
| State | Published - 2020 |
ASJC Scopus subject areas
- Applied Mathematics
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Germain, P., Harrop-Griffiths, B., & Marzuola, J. L. (2020). Compactons and their variational properties for degenerate kdv and nls in dimension 1. Quarterly of Applied Mathematics, 78, 1-32. [1538]. https://doi.org/10.1090/QAM/1538