Emergent soliton-like solutions in the parametrically driven 1-D nonlinear Schr\"odinger equation

K Dileep; S Murugesh

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arXiv · 2301.03237

Emergent soliton-like solutions in the parametrically driven 1-D nonlinear Schr\"odinger equation

K Dileep·S Murugesh

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Abstract

We numerically investigate the long time dynamics of spatially periodic breather solutions of the 1-D nonlinear Schr\"odinger equation under parametric forcing of the form $f(x)=f_0 \exp(iKx)$ along with dissipation. In the absence of dissipation, robust soliton-like excitations are observed that travel with constant amplitude and velocity. With dissipation, these solitons lose energy (and amplitude) yet gain speed - a characteristic not observed in an ordinary soliton. Moreover, these novel solitons are found to be stable against random perturbations.

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K Dileep, S Murugesh. 2023-01-09. Emergent soliton-like solutions in the parametrically driven 1-D nonlinear Schr\"odinger equation. https://arxiv.org/abs/2301.03237

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