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arXiv · 1709.05031

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

Pierre Germain·Benjamin Harrop-Griffiths·Jeremy L. Marzuola
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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 non-degenerate 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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Pierre Germain, Benjamin Harrop-Griffiths, Jeremy L. Marzuola. 2017-09-15. Compactons and their variational properties for degenerate KdV and NLS in dimension 1. https://arxiv.org/abs/1709.05031

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