Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2002-05-17
Physical Review E (Rapid Communications) 65, 065601(R) (2002)
Nonlinear Sciences
Pattern Formation and Solitons
4 pages, 3 figures. To appear in Phys. Rev. E (Rapid Comm.)
Scientific paper
10.1103/PhysRevE.65.065601
We investigate the dynamics of the sine-Gordon solitons perturbed by spatiotemporal external forces. We prove the existence of internal (shape) modes of sine-Gordon solitons when they are in the presence of inhomogeneous space-dependent external forces, provided some conditions (for these forces) hold. Additional periodic time-dependent forces can sustain oscillations of the soliton width. We show that, in some cases, the internal mode even can become unstable, causing the soliton to decay in an antisoliton and two solitons. In general, in the presence of spatiotemporal forces the soliton behaves as a deformable (non-rigid) object. A soliton moving in an array of inhomogeneities can also present sustained oscillations of its width. There are very important phenomena (like the soliton-antisoliton collisions) where the existence of internal modes plays a crucial role.
Bellorin A.
Gonzalez Jose A.
Guerrero L. E.
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