18 citations · 24 across the 6 of their papers we have counts for
6 papers
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…
On the Whitham Equations for the Defocusing Complex Modified KdV Equation
Yuji Kodama, V. U. Pierce, Fei-Ran Tian
We study the Whitham equations for the defocusing complex modified KdV (mKdV) equation. These Whitham equations are quasilinear hyperbolic equations and they describe the averaged…
Self-Similar Solutions of the Non-Strictly Hyperbolic Whitham Equations for the KdV Hierarchy
V. U. Pierce, Fei-Ran Tian
We study the Whitham equations for all the higher order KdV equations. The Whitham equations are neither strictly hyperbolic nor genuinely nonlinear. We are interested in the solut…
Large Time Behavior of the Zero Dispersion Limit of the Fifth Order KdV Equation
V. U. Pierce, Fei-Ran Tian
We study the zero dispersion limit of the fifth order KdV equations when time is sufficiently large. In general, the weak limit may be described by an arbitrary odd number of hyper…
Self-Similar Solutions of the Non-Strictly Hyperbolic Whitham Equations
V. U. Pierce, Fei-Ran Tian
We study the Whitham equations for the fifth order KdV equation. The equations are neither strictly hyperbolic nor genuinely nonlinear. We are interested in the solution of the Whi…
Large Parameter Behavior of Equilibrium Measures
Tamara Grava, Fei-Ran Tian
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…