Abstract:
The talk is devoted to the study of traveling waves for a semilinear
parabolic equation, the nonlinear term of which can have both a local
and a non-local character. This is primarily the equation considered in
the seminal work of Kolmogorov, Petrovskii and Piskunov. We consider a
class of nonlinearities that arise in connection with the development of
applications in voting models based on branching Brownian motion. We
present an analytical solution that generalizes the results of Ablowitz
and Kaliappan to a broader class of equations. The method of
constructing exact solutions also applies to the nonlocal modification
of the KPP equation that arises from population dynamics.
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