We predict theoretically that, via a resonance mechanism, stable moving solitons exist in a discrete (1+1)-dimensional nonlinear Schrödinger (Ablowitz-Ladik) equation with dissipation and an ac driving term in the form of a standing wave. Agreement between the predicted threshold (minimum) values of the strength of the drive which is able to sustain the moving solitons and those measured in direct numerical simulations is excellent. Our results show an example of multistability in damped, standing-wave-driven systems. The dynamical instability for the motion of solitons in the unstable regimes is also analyzed.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics