Existence and stability of driven and damped phase-locked NLS-solitons and SG-breathers

Abstract

The spatio-temporal behaviors of possible solutions of driven and damped nonlinear Schrodinger and sine-Gordon equations are analyzed. In the first part, the nonlinear Schrodinger equation is considered also as the limiting case corresponding to weak driving and damping in the sine-Gordon equation, with driving frequency close to one. It is shown that in this limit a phase-locked breather with m/n = 1/1 exists and undergoes period-doubling bifurcations. The close analogy to the dynamics of a phase-locked Schrodinger soliton is demonstrated in detail. In the second part, for smaller driving frequencies, the existence and stability of subharmonically phase-locked breathers is discussed. The quasi-periodic route to chaos is re-investigated and special attention is given to the length-dependence of the results. The findings are compared with predictions of simpler models in nonlinear dynamics. The whole paper consists of analytical and numerical results. For the latter, improved diagnostic tools have been developed.