A numerical approach to blow-up issues for dispersive perturbations of Burgers%26apos; equation

作者：Klein Christian; Saut Jean Claude

来源：Physica D: Nonlinear Phenomena , 2015, 295: 46-65.

DOI：10.1016/j.physd.2014.12.004

• Fractional Korteweg-de Vries equations
• Fractional BBM equations
• Whitham equations
• Solitons
• Blow-up

We provide a detailed numerical study of various issues pertaining to the dynamics of the Burgers' equation perturbed by a weak dispersive term: blow-up in finite time versus global existence, nature of the blow-up, existence for "long" times, and the decomposition of the initial data into solitary waves plus radiation. We numerically construct solitary waves for fractional Korteweg-de Vries equations.

• 出版日期2015-3-1