Invariant subspaces and generalized functional separable solutions to the two-component b-family system

https://doi.org/10.1016/S0252-9602(16)30037-6Get rights and content

Abstract

Invariant subspace method is exploited to obtain exact solutions of the two-component b-family system. It is shown that the two-component b-family system admits the generalized functional separable solutions. Furthermore, blow up and behavior of those exact solutions are also investigated.

References (38)

  • R Camassa et al.

    An integrable shallow water equation with peaked solitons

    Phys Rev Lett

    (1993)
  • A Constantin et al.

    The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations

    Arch Ration Mech Anal

    (2009)
  • M Chen et al.

    A two-component generalization of the Camassa-Holm equation and its solutions

    Lett Math Phys

    (2006)
  • J Eschel et al.

    Well-posedness and blow-up phenomena for the 2-component Camassa-Holm equation

    Discrete Contin Dyn Syst Ser A

    (2007)
  • M Yuen

    Self-similar blow up solutions to the two-component Camassa-Holm equations

    J Math Phys

    (2010)
  • A S Fokas et al.

    Asymptotic integrability of water waves

    Phys Rev Lett

    (1996)
  • R Dullin et al.

    An integrable shallow water equation with linear and nonlinear dispersion

    Phys Rev Lett

    (2001)
  • R S Johnson

    Camassa-Holm, Korteweg-de Vries and related models for water waves

    J Fluid Mech

    (2002)
  • A Constantin

    Existence of permanent and breaking waves for a shallow water equation: a geometric approach

    Ann Inst Fourier (Grenoble)

    (2000)

    • Cited by (0)

    This work is supported by NSFC (11471260) and the Foundation of Shannxi Education Committee (12JK0850).

    View full text
    Copyright © 2016 Wuhan Institute of Physics and Mathematics. Published by Elsevier Ltd. All rights reserved.