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The nonlinear Schrödinger equation created by the vibrations of an elastic plate and its dimensional expansion

Pages: 415 - 426, Issue special, November 2013

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Shuya Kanagawa - Department of Mathematics, Tokyo City University, 1-28-1 Tamazutsumi, Setagaya-ku, Tokyo 158-8557, Japan (email)
Ben T. Nohara - Department of Information Science, Tokyo City University, 1-28-1 Tamazutsumi, Setagaya-ku, Tokyo 158-8557, Japan (email)

Abstract: We first survey the two-dimensional governing equation that describes the propagation of a wave packet on an elastic plate using the method of multiple scales by [13]. We next expand the governing equation to the multi-dimensional case not only in the sense of mathematical science but also engineering.

Keywords:  Schrödinger equation, Ginzburg-Landau equation, elastic plate, envelope, governing equation, monochromatic wave, bichromatic wave.
Mathematics Subject Classification:  Primary: 35L05; Secondary: 35Q55.

Received: September 2012;      Revised: April 2013;      Published: November 2013.

 References