Singularity formation in the generalized Benjamin-Ono equation

Jerry Bona; H. Kalisch

doi:10.3934/dcds.2004.11.27

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2004, Volume 11, Issue 1: 27-45. Doi: 10.3934/dcds.2004.11.27

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Singularity formation in the generalized Benjamin-Ono equation

Jerry Bona^1, and
H. Kalisch^2,

1.
Department of Mathematics, Statistics and Computer Science, The University of Illinois at Chicago , 851 S. Morgan Street MC 249, Chicago, Illinois 60607-7045
2.
Centre for Mathematical Sciences, Lund University, 221 00 Lund

Received: February 28, 2003

Revised: January 31, 2004

Published: December 2003

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Abstract

A Fourier-collocation scheme is used to approximate solutions to the generalized Benjamin-Ono equation $u_t + u^pu_x - H u_{x x} = 0$. The numerical simulation suggests that the equation features smooth solutions that become unbounded in finite time.

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Mathematics Subject Classification: 35B60.

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