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

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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


Ben T. Nohara

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


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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