Synchronization of traveling waves in a dispersive system of weakly coupled equations

All-Russian conference on Nonlinear Waves: Theory and New Applications

Makridin, Z.V.^1,2 ; Makarenko, N.I.^1,2

Lavrentyev Institute of Hydrodynamics, Novosibirsk

630090, Russia^1

Novosibirsk State University, Novosibirsk

630090, Russia^2

关键词: Bifurcation equations;    Coupled differential equations;    Coupled equation;    Dispersive media;    Dispersive systems;    Group symmetries;    Nonlinear perturbations;    Periodic solution;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/722/1/012028/pdf
DOI  :  10.1088/1742-6596/722/1/012028

来源: IOP

【 摘 要 】

The system of weakly coupled differential equations describing traveling waves in dispersive media is considered. The Lyapunov - Schmidt construction is used to study the branching of cnoidal-type periodic solutions. The analysis of bifurcation equations uses the group symmetry and cosymmetry of original equations. Sufficient condition for existence of the phase-shifted modes of cnoidal waves is formulated in terms of the Pontryagin's function determined by the nonlinear perturbation terms.