Abstract: A new periodic wave solution in terms of Riemann theta functions to the elliptic equation is presented, then by using this solution and the improved generalized F-expansion method, some exact solutions in terms of Riemann theta functions to the KdV-Burgers-Kuramoto(KBK) equation are obtained with the aid of Mathematica, their properties and profiles are displayed in their figures. To ...

The Kuramoto model describes the collective dynamics of a system of coupled oscillators. An α-Kuramoto partition is a graph partition induced by the Kuramoto model, when the oscillators include a phase frustration parameter. We prove that every equitable partition is an α-Kuramoto partition, but that the converse does necessarily not hold. We give an exact characterisation of α-Kuramoto biparti...

In this note, we announce a general result resolving the long-standing question of nonlinear modulational stability, or stability with respect to localized perturbations, of periodic travelingwave solutions of the generalized Kuramoto–Sivashinski equation, establishing that spectral modulational stability, defined in the standard way, implies nonlinear modulational stability with sharp rates of...