Self-similar solutions of the non-strictly hyperbolic Whitham equations

Pierce, Virgil U.; Tian, Fei-Ran

Commun. Math. Sci., Tome 4 (2006) no. 1, p. 799-822 / Harvested from Project Euclid

Résumé

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.

Publié le : 2006-12-14
Classification: Zero dispersion limit, Whitham equations, non-strictly hyperbolic equations, 35Q53, 35C05, 35L65, 35L67

@article{1175797612,
     author = {Pierce, Virgil U. and Tian, Fei-Ran},
     title = {Self-similar solutions of the non-strictly hyperbolic Whitham equations},
     journal = {Commun. Math. Sci.},
     volume = {4},
     number = {1},
     year = {2006},
     pages = { 799-822},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1175797612}
}

Pierce, Virgil U.; Tian, Fei-Ran. Self-similar solutions of the non-strictly hyperbolic Whitham equations. Commun. Math. Sci., Tome 4 (2006) no. 1, pp.  799-822. http://gdmltest.u-ga.fr/item/1175797612/