Numerical Analyses of the Localized Structures on an Uneven Bottom Associated with the Davey-Stewartson 1 Equations
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Publication:2703637
DOI10.1143/JPSJ.65.1598zbMath0965.35143arXivsolv-int/9508004OpenAlexW2085555091MaRDI QIDQ2703637
Tetsu Yajima, Katsuhiro Nishinari
Publication date: 2 April 2001
Published in: Journal of the Physical Society of Japan (Search for Journal in Brave)
Abstract: The Davey-Stewartson (DS) equations with a perturbation term are presented by taking a fluid system as an example on an uneven bottom. Stability of dromions, solutions of the DS equations with localized structures, against the perturbation is investigated numerically. Dromions decay exponentially under an effect of the perturbation, while they travel stably after the effect disappears. The decay ratio of dromions is found to have relation to velocities of dromions. The important role played by the mean flow, which acts as an external force to the system, is discussed. These results show that dromions are quite stable as a localized structure in two dimensions, and they are expected to observed in various physical systems such as fluid or plasma systems.
Full work available at URL: https://arxiv.org/abs/solv-int/9508004
KdV equations (Korteweg-de Vries equations) (35Q53) Special approximation methods (nonlinear Galerkin, etc.) for infinite-dimensional dissipative dynamical systems (37L65)
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