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 Waves and Solitons #Nonlinear Photonic Systems

paper · pdf · doi:10.48550/arxiv.1002.3178

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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