Communications in Mathematical Sciences
Volume 4 (2006)
Self-similar solutions of the non-strictly hyperbolic Whitham equations
Pages: 799 – 822
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 Whitham equations when the initial values are given by a step function. We classify the step-like initial data into eight different types. We construct self-similar solutions for each type.
Zero dispersion limit; Whitham equations; non-strictly hyperbolic equations
2010 Mathematics Subject Classification
Primary 35Q53. Secondary 35C05, 35L65, 35L67.