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For the case of sufficiently small approach velocity and sufficiently large values of the dissipative cross-coupling between the counter-propagating 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 quasi-one-dimensional objects. As a model, we use coupled cubic\u2013quintic complex Ginzburg\u2013Landau 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\u2013quintic complex Ginzburg\u2013Landau equation with effective parameters.<\/jats:p>","DOI":"10.1098\/rsta.2015.0115","type":"journal-article","created":{"date-parts":[[2015,11,2]],"date-time":"2015-11-02T21:03:58Z","timestamp":1446498238000},"page":"20150115","update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["Non-unique results of collisions of quasi-one-dimensional dissipative solitons"],"prefix":"10.1098","volume":"373","author":[{"given":"Orazio","family":"Descalzi","sequence":"first","affiliation":[{"name":"Complex Systems Group, Facultad de Ingenier\u00eda y Ciencias Aplicadas, Universidad de los Andes, Av. 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