Traveling Wave Solutions to the Burgers-αβ Equations
B Moon - Advanced Nonlinear Studies, 2016 - degruyter.com
Advanced Nonlinear Studies, 2016•degruyter.com
The Burgers-αβ equation, which was first introduced by Holm and Staley, is considered in
the special case where ν= 0 and b= 3. Traveling wave solutions are classified to the Burgers-
αβ equation containing four parameters b, α, ν, and β, which is a nonintegrable nonlinear
partial differential equation that coincides with the usual Burgers equation and viscous b-
family of peakon equation, respectively, for two specific choices of the parameter β= 0 and
β= 1. Under the decay condition, it is shown that there are smooth, peaked and cusped …
the special case where ν= 0 and b= 3. Traveling wave solutions are classified to the Burgers-
αβ equation containing four parameters b, α, ν, and β, which is a nonintegrable nonlinear
partial differential equation that coincides with the usual Burgers equation and viscous b-
family of peakon equation, respectively, for two specific choices of the parameter β= 0 and
β= 1. Under the decay condition, it is shown that there are smooth, peaked and cusped …
Abstract
The Burgers-αβ equation, which was first introduced by Holm and Staley , is considered in the special case where and . Traveling wave solutions are classified to the Burgers-αβ equation containing four parameters , and β, which is a nonintegrable nonlinear partial differential equation that coincides with the usual Burgers equation and viscous b-family of peakon equation, respectively, for two specific choices of the parameter and . Under the decay condition, it is shown that there are smooth, peaked and cusped traveling wave solutions of the Burgers-αβ equation with and depending on the parameter β. Moreover, all traveling wave solutions without the decay condition are parametrized by the integration constant . In an appropriate limit , the previously known traveling wave solutions of the Degasperis–Procesi equation are recovered.
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