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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

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  March 2003 Revised  February 2004 Published  April 2004

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 and Continuous Dynamical Systems, 2004, 11 (1) : 27-45. doi: 10.3934/dcds.2004.11.27
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