TY - JOUR
T1 - Initial value problem of the Whitham equations for the Camassa-Holm equation
JF - Physica D 238 (2009) 55-66
Y1 - 2009
A1 - Tamara Grava
A1 - Virgil U. Pierce
A1 - Fei-Ran Tian
AB - 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 of the Whitham equations. When the initial values are given by a step function, the Whitham solution is self-similar. When the initial values are given by a smooth function, the Whitham solution exists within a cusp in the x-t plane. On the boundary of the cusp, the Whitham equation matches the Burgers solution, which exists outside the cusp.
PB - Elsevier
UR - http://hdl.handle.net/1963/3429
U1 - 906
U2 - Mathematics
U3 - Mathematical Physics
ER -