Collective coordinates theory for discrete soliton ratchets in the sine-Gordon model.
A collective coordinate theory is developed for soliton ratchets in the damped discrete sine-Gordon model driven by a biharmonic force. An ansatz with two collective coordinates, namely the center and the width of the soliton, is assumed as an approximated solution of the discrete nonlinear equation. The dynamical equations of these two collective coordinates, obtained by means of the generalized travelling wave method, explain the mechanism underlying the soliton ratchet and capture qualitatively all the main features of this phenomenon. The numerical simulation of these equations accounts for the existence of a nonzero depinning threshold, the nonsinusoidal behavior of the average velocity as a function of the relative phase between the harmonics of the driver, the nonmonotonic dependence of the average velocity on the damping, and the existence of nontransporting regimes beyond the depinning threshold. In particular, it provides a good description of the intriguing and complex pattern of subspaces corresponding to different dynamical regimes in parameter space.
Departamento de Física Aplicada I, E.P.S., Universidad de Sevilla, Virgen de África 7, 41011, Sevilla, Spain.
Bernardo
B
Sánchez-Rey
Departamento de Física Aplicada I, E.P.S., Universidad de Sevilla, Virgen de África 7, 41011, Sevilla, Spain and Instituto de Matemáticas de la Universidad de Sevilla (IMUS). Edificio Celestino Mutis. Avda. Reina Mercedes s/n, 41012-Sevilla, Spain.
Niurka R
NR
Quintero
Departamento de Física Aplicada I, E.P.S., Universidad de Sevilla, Virgen de África 7, 41011, Sevilla, Spain and Instituto de Matemáticas de la Universidad de Sevilla (IMUS). Edificio Celestino Mutis. Avda. Reina Mercedes s/n, 41012-Sevilla, Spain.
Jesús
J
Cuevas-Maraver
Instituto Nacional de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, Brazil.
Miguel A
MA
Alejo