AbstractThe Burgers-αβ
equation, which was first introduced by Holm and Staley
[4], is considered in the special case where ${\nu=0}$ and ${b=3}$. Traveling wave solutions are classified to the Burgers-αβ equation containing four parameters ${b,\alpha,\nu}$, 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 ${\beta=0}$ and ${\beta=1}$.
Under the decay condition, it is shown that there are smooth, peaked and cusped traveling wave solutions
of the Burgers-αβ equation with ${\nu=0}$ and ${b=3}$ depending on the parameter β. Moreover, all traveling wave solutions without the decay condition are parametrized by the integration constant ${k_{1}\in\mathbb{R}}$. In an appropriate limit ${\beta=1}$, the previously known traveling wave solutions of the Degasperis–Procesi equation are recovered.
Bifurcations of solitary wave solutions for (two and three)-dimensional nonlinear partial differential equation in quantum and magnetized plasma by using two different methods
