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

Shuya Kanagawa; Ben T. Nohara

doi:10.3934/proc.2013.2013.415

Article Contents

2013, Volume 2013: 415-426. Doi: 10.3934/proc.2013.2013.415 open access

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

Shuya Kanagawa^1, and
Ben T. Nohara^2,

1.
Department of Mathematics, Tokyo City University, 1-28-1 Tamazutsumi, Setagaya-ku, Tokyo 158-8557
2.
Department of Information Science, Tokyo City University, 1-28-1 Tamazutsumi, Setagaya-ku, Tokyo 158-8557

Received: August 31, 2012

Revised: March 31, 2013

Published: October 2013

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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.

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Mathematics Subject Classification: Primary: 35L05; Secondary: 35Q55.

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References

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