ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations
and
Control Processes

Robustness of Governing Equations of Envelope Surface Created by Nearly Monochromatic Waves

Author(s):

Ben T. Nohara

Musashi Institute of Technology
Department of Electronic and Computer Engineering
Tamazutsumi, Setagaya, Tokyo 158-8557
Japan
Phone: (03)3703-3111 Fax: (03)5707-2147

drben@ac.cs.musashi-tech.ac.jp

Abstract:

In this paper the author deals with the Schrödinger equation of the two-dimensional envelope surfaces of the water waves and discusses the robustness about the propagation direction of this equation. In the field of the water and/or the plasma, the Schrödinger equation governs the envelope created by the nearly monochromatic waves, which energy is almost concentrated in a single frequency. The two-dimensional Schrödinger equation, which governs the envelope surface instead of the envelope of the one-dimensional system, is obtained through the straightforward process from the one-dimensional system. The obtained two-dimensional Schrödinger equation contains the parameter of the propagation direction. The author shows that the two-dimensional Schrödinger equation is robust about the propagation direction, i.e., the small variation of the propagation direction makes no change of the original equation.

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