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

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

doi:10.1090/QAM/1538

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

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

Mathematics

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.1090/QAM/1538
State	Published - 2020

ASJC Scopus subject areas

Applied Mathematics

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

Abstract

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