Compactons and their variational properties for degenerate KdV and NLS in dimension 1
Compactons and their variational properties for degenerate KdV and NLS in dimension 1
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DOI：
10.1090/qam/1538
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发表时间：
2017-09
影响因子：
0.8
通讯作者：
P. Germain;Benjamin Harrop-Griffiths;J. Marzuola
中科院分区：
文献类型：
--
作者：
P. Germain;Benjamin Harrop-Griffiths;J. Marzuola
本文分析了一类KdV型和NLS型退化色散方程的定解和行波解。与非退化KdV和NLS方程的标准孤子解形成鲜明对比的是，这里研究的椭圆算子的退化允许紧支撑的稳定或旅行状态。当我们在$1$维工作时，ODE方法适用，但是考虑的模型具有形式上保守的哈密顿量，质量和动量泛函，这也允许变分分析。
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.