@article {2009,
title = {Initial value problem of the Whitham equations for the Camassa-Holm equation},
journal = {Physica D 238 (2009) 55-66},
number = {arXiv.org;0805.2558v1},
year = {2009},
publisher = {Elsevier},
abstract = {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.},
doi = {10.1016/j.physd.2008.08.016},
url = {http://hdl.handle.net/1963/3429},
author = {Tamara Grava and Virgil U. Pierce and Fei-Ran Tian}
}
@article {2006,
title = {Large Parameter Behavior of Equilibrium Measures},
number = {SISSA;92/2005/FM},
year = {2006},
abstract = {We study the equilibrium measure for a logarithmic potential in the presence of an external field V*(x) + tp(x), where t is a parameter, V*(x) is a smooth function and p(x) a monic polynomial. When p(x) is of an odd degree, the equilibrium measure is shown to be supported on a single interval as |t| is sufficiently large. When p(x) is of an even degree, the equilibrium measure is supported on two disjoint intervals as t is negatively large; it is supported on a single interval for convex p(x) as t is positively large and is likely to be supported on multiple disjoint intervals for non-convex p(x).},
url = {http://hdl.handle.net/1963/1789},
author = {Tamara Grava and Fei-Ran Tian}
}