18 citations · 18 across the 3 of their papers we have counts for
3 papers
math-ph2009
Numerical Solution of the Small Dispersion Limit of the Camassa-Holm and Whitham Equations and Multiscale Expansions
S. Abenda, T. Grava, C. Klein
The small dispersion limit of solutions to the Camassa-Holm (CH) equation is characterized by the appearance of a zone of rapid modulated oscillations. An asymptotic description of…
math-ph2008
Painleve II asymptotics near the leading edge of the oscillatory zone for the Korteweg-de Vries equation in the small dispersion limit
T. Claeys, T. Grava
In the small dispersion limit, solutions to the Korteweg-de Vries equation develop an interval of fast oscillations after a certain time. We obtain a universal asymptotic expansion…
nlin.SI2008★ 18 cited
Initial Value Problem of the Whitham Equations for the Camassa-Holm Equation
Tamara Grava, V. U. Pierce, Fei-Ran Tian
We study the Whitham equations for the Camassa-Holm equation. The equations are neither strictly hyperbolic nor genuinely nonlinear. We are interested in the initial value problem…