Differential and Integral Equations

On the support of solutions to the NLS-KdV system

José Jiménez Urrea

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Abstract

It is shown that if $(u,v)$ is a sufficiently smooth solution of the initial value problem associated with the Schrödinger-Korteweg-de Vries system such that there exist $a, b\in\mathbb{R}$ with $\operatorname{supp}u(t_j)\subseteq(a,\infty)$ (or$(-\infty,a)$) and $\operatorname{supp}v(t_j)\subseteq(b,\infty)$ (or $(-\infty,b)$), for $j=1,2 \ (t_1\neq t_2)$, then $u\equiv v\equiv0$.

Article information

Source
Differential Integral Equations, Volume 25, Number 7/8 (2012), 611-618.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356012653

Mathematical Reviews number (MathSciNet)
MR2975685

Zentralblatt MATH identifier
1265.35305

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10] 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Citation

Urrea, José Jiménez. On the support of solutions to the NLS-KdV system. Differential Integral Equations 25 (2012), no. 7/8, 611--618. https://projecteuclid.org/euclid.die/1356012653


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