On long-time behavior of solutions of the Zakharov–Rubenchik/Benney–Roskes system

Abstract We study decay properties for solutions to the initial value problem associated with the one-dimensional Zakharov–Rubenchik/Benney–Roskes (ZR/BR) system. We prove time-integrability in growing compact intervals of size t r , r < 2/3, centered on some characteristic curves coming from the...

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Bibliographic Details
Published inNonlinearity Vol. 34; no. 11; pp. 7750 - 7777
Main Authors Martínez, María E, Palacios, José M
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.11.2021
Subjects
decay
long-time behavior
scattering
Zakharov–Rubenchik/Benney–Roskes
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Summary:Abstract We study decay properties for solutions to the initial value problem associated with the one-dimensional Zakharov–Rubenchik/Benney–Roskes (ZR/BR) system. We prove time-integrability in growing compact intervals of size t r , r < 2/3, centered on some characteristic curves coming from the underlying transport equations associated with the ZR/BR system. Additionally, we prove decay to zero of the local energy-norm in so-called far-field regions. Our results are independent of the size of the initial data and do not require any parity condition.
Bibliography:London Mathematical Society
NON-105197.R1
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/ac288c