We investigate collisions of quasi-one-dimensional dissipative solitons (DSs) for a large class of initial conditions, which are not temporally asymptotic quasi-one-dimensional DSs. For the case of sufficiently small approach velocity and sufficiently large values of the dissipative cross-coupling between the counterpropagating DSs, we find non-unique results for the outcome of collisions. We demonstrate that these non-unique results are intrinsically related to a modulation instability along the crest of the quasione- dimensional objects. As a model, we use coupled cubic quintic complex Ginzburg Landau equations. Among the final results found are stationary and oscillatory compound states as well as more complex assemblies consisting of quasi-one-dimensional and localized states. We analyse to what extent the final results can be described by the solutions of one cubic quintic complex Ginzburg Landau equation with effective parameters.
|Journal||Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences|
|State||Published - 13 Dec 2015|
Bibliographical notePublisher Copyright:
© 2015 The Author(s) Published by the Royal Society. All rights reserved.
- Complex Ginzburg Landau equation
- Dissipative solitons
- Localized structures