Singularity formation in the generalized Benjamin-Ono equation

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January 2004, 11(1): 27-45. doi: 10.3934/dcds.2004.11.27

Singularity formation in the generalized Benjamin-Ono equation

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 March 2003 Revised February 2004 Published April 2004

Abstract
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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.

Keywords: integro-differential equations, singularity formation., Nonlinear waves, Fourier-collocation.

Mathematics Subject Classification: 35B6.

Citation: Jerry Bona, H. Kalisch. Singularity formation in the generalized Benjamin-Ono equation. Discrete & Continuous Dynamical Systems - A, 2004, 11 (1) : 27-45. doi: 10.3934/dcds.2004.11.27

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