On the zero-dispersion limit of the Benjamin-Ono Cauchy problem for positive initial data

2010/02/17 by Peter D. Miller, Miller, Peter D., Zhengjie Xu +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #nlin.PS #nlin.SI

paper · pdf · doi:10.48550/arxiv.1002.3178

54 pages, 11 figures

arxiv created 2010/02/17 · arxiv updated 2010/02/26

Abstract

We study the Cauchy initial-value problem for the Benjamin-Ono equation in the zero-disperion limit, and we establish the existence of this limit in a certain weak sense by developing an appropriate analogue of the method invented by Lax and Levermore to analyze the corresponding limit for the Korteweg-de Vries equation.

Citations

• On the Distribution of the Roots of Certain Symmetric Matrices

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• The zero-dispersion limit for the Benjamin--Ono equation on the circle

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