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On nonlinear wave envelopes of permanent form near a caustic

Published online by Cambridge University Press:  26 April 2006

T. R. Akylas  and
T.-J. Kung
T. R. Akylas
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
T.-J. Kung
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
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Abstract

In the vicinity of a caustic of a dispersive wave system, where the group velocity is stationary and hence dispersive effects are relatively weak, the nonlinear Schrödinger equation (NLS) breaks down, and the propagation of the envelope of a finiteamplitude wavepacket is governed by a modified nonlinear Schrödinger equation (MNLS). On the basis of the MNLS, a search for wave envelopes of permanent form is made near a caustic. It is shown that possible solitary wave envelopes satisfy a nonlinear eigenvalue problem. Numerical evidence is presented of symmetric, double-hump solitary-wave solutions. Also, a variety of periodic envelopes are computed. These findings are discussed in connection with previous analytical and numerical work.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 214 , May 1990 , pp. 489 - 502
Copyright
© 1990 Cambridge University Press

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