Compactons and their variational properties for degenerate KdV and NLS in dimension 1

Germain, Pierre; Harrop-Griffiths, Benjamin; Marzuola, Jeremy

doi:10.1090/qam/1538

Authors: Pierre Germain, Benjamin Harrop-Griffiths and Jeremy L. Marzuola
Journal: Quart. Appl. Math. 78 (2020), 1-32
MSC (2010): Primary 35Q53, 35Q55
DOI: https://doi.org/10.1090/qam/1538
Published electronically: April 17, 2019
MathSciNet review: 4042218
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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.

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