TY - RPRT
T1 - Numerical Solution of the Small Dispersion Limit of the Camassa-Holm and Whitham Equations and Multiscale Expansions
Y1 - 2010
A1 - Simonetta Abenda
A1 - Tamara Grava
A1 - Christian Klein
AB - 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 these oscillations is given, for short times, by the one-phase solution to the CH equation, where the branch points of the corresponding elliptic curve depend on the physical coordinates via the Whitham equations. We present a conjecture for the phase of the asymptotic solution. A numerical study of this limit for smooth hump-like initial data provides strong evidence for the validity of this conjecture....
UR - http://hdl.handle.net/1963/3840
U1 - 487
U2 - Mathematics
U3 - Mathematical Physics
ER -