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

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

2010-02-17

arxiv.org/abs/1002.3178v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

54 pages, 11 figures

Scientific paper

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.

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