The current work is devoted to studying the dynamical behavior of Sakovich equation with beta derivatives. We announce conditions problem parameters leading existence periodic, solitary, and kink solutions by applying qualitative theory planar systems. Based on these conditions, we construct some new integrating conserved quantity along possible interval real wave propagation in order obtain th...

We study the existence, uniqueness, and asymptotic stability of time periodic traveling wave solutions to a periodic diffusive Lotka-Volterra competition system. Under certain conditions, we prove that there exists a maximal wave speed c(*) such that for each wave speed c ≤ c(*), there is a time periodic traveling wave connecting two semi-trivial periodic solutions of the corresponding kinetic ...

We study the existence, uniqueness, and asymptotic stability of time periodic traveling wave solutions to a class of periodic advection–reaction–diffusion systems. Under certain conditions, we prove that there exists a maximal wave speed c∗ such that for each wave speed c ≤ c∗, there is a time periodic traveling wave connecting two periodic solutions of the corresponding kinetic system. It is s...

We prove the existence of a global bifurcation branch of 2π-periodic, smooth, traveling-wave solutions of the Whitham equation. It is shown that any subset of solutions in the global branch contains a sequence which converges uniformly to some solution of Hölder class C, α < 1 2 . Bifurcation formulas are given, as well as some properties along the global bifurcation branch. In addition, a spec...