Structural Stability of Perturbed mKdV Solitons

Abstract

Periodic perturbations are applied to the homoc\inic orbits corresponding to solitons of the modified Korteweg-de Vries (mKdV) equation, which is significant in plasma physics and lattice models. It is observed that for certain distinct frequencies the homoclinic orbits do not split into stable and unstable manifolds, which means absence of horseshoes and chaos. The analysis is performed on a travelling wave reduced form of the mKdV equation both by standard application of the Melnikov method as well as numerical generation of POincare maps. In particular, the geometry of the homoclinic orbits and their structural changes under perturbations is investigated.