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03/03/04 Colloquium
DR. PHILIPPE GUYENNE
DEPARTMENT OF MATHEMATICS
McMASTER UNIVERSITY, CANADA
DEPARTMENT OF MATHEMATICS
McMASTER UNIVERSITY, CANADA
Wave Turbulence in One-Dimensional Models
Abstract: A two-parameter nonlinear dispersive wave equation proposed by Majda, McLaughlin and Tabak (1997) is studied analytically and numerically as a model for testing the validity of weak turbulence theory. Kolmogorov-type solutions for the energy spectrum are determined explicityly and compared with numerical results. These show a strong dependence on the sign of the nonlinear term. In one case, there is agreement with the throey. In the other, there is disagreement. Possible explanations for this discrepancy will be given such as the emergence of coherent structures: wave collapse and quasi-solitons.