Soliton solutions of driven non-linear and higher order non-linear Schrödinger equations

Details Soliton solutions of driven non-linear and higher order non-linear Schrödinger equations Soliton solutions of driven non-linear and higher order non-linear Schrödinger equations

2005-11-09

arxiv.org/abs/nlin/0511014v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

10 pages, 2 figures

Scientific paper

We analyse the structure of the exact, dark and bright soliton solutions of the driven non-linear Schr\"odinger equation. It is found that, a wide class of solutions of the higher order non-linear Schr\"odinger equation with a source can also be obtained through the above procedure. Distinct parameter ranges, allowing the existence of these solutions, phase locked with their respective sources, are delineated. Conditions for obtaining non-propagating solutions are found to be quite different for both the equations. A special case, where the scale of the soliton emerges as a free parameter, is obtained and the condition under which solitons can develop singularity is pointed out. We also study the highly restrictive structure of the localised solutions, when the phase and amplitude get coupled.

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