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Generalized &Thetas;-Parameter Peakon Solutions For A Cubic Camassa-Holm Model, Michael Rippe
Generalized &Thetas;-Parameter Peakon Solutions For A Cubic Camassa-Holm Model, Michael Rippe
Theses and Dissertations
In this paper we outline a method for obtaining generalized peakon solutions for a cubic Camassa-Holm model originally introduced by Fokas (1995) and recently shown to have a Lax pair representation and bi-Hamiltonian structure by Qiao et al (2012). By considering an amended signum function—denoted sgn &thetas;(x)—where sgn(0) = &thetas; for a constant &thetas;, we explore new generalized peakon solutions for this model. In this context, all previous peakon solutions are of the case &thetas; = 0. Further, we aim to analyze the algebraic quadratic equation resulting from a substitution of the single-peakon ansatz equipped with our amended …