{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T11:20:27Z","timestamp":1753874427092,"version":"3.41.2"},"reference-count":70,"publisher":"AIP Publishing","issue":"12","funder":[{"DOI":"10.13039\/501100002850","name":"Fondo Nacional de Desarrollo Cient\u00edfico y Tecnol\u00f3gico","doi-asserted-by":"publisher","award":["1200357"],"award-info":[{"award-number":["1200357"]}],"id":[{"id":"10.13039\/501100002850","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2022,12,1]]},"abstract":"<jats:p>We study the time-dependent behavior of dissipative solitons (DSs) stabilized by nonlinear gradient terms. Two cases are investigated: first, the case of the presence of a Raman term, and second, the simultaneous presence of two nonlinear gradient terms, the Raman term and the dispersion of nonlinear gain. As possible types of time-dependence, we find a number of different possibilities including periodic behavior, quasi-periodic behavior, and also chaos. These different types of time-dependence are found to form quite frequently from a window structure of alternating behavior, for example, of periodic and quasi-periodic behaviors. To analyze the time dependence, we exploit extensively time series and Fourier transforms. We discuss in detail quantitatively the question whether all the DSs found for the cubic complex Ginzburg\u2013Landau equation with nonlinear gradient terms are generic, meaning whether they are stable against structural perturbations, for example, to the additions of a small quintic perturbation as it arises naturally in an envelope equation framework. Finally, we examine to what extent it is possible to have different types of DSs for fixed parameter values in the equation by just varying the initial conditions, for example, by using narrow and high vs broad and low amplitudes. These results indicate an overlapping multi-basin structure in parameter space.<\/jats:p>","DOI":"10.1063\/5.0118348","type":"journal-article","created":{"date-parts":[[2022,12,1]],"date-time":"2022-12-01T16:28:30Z","timestamp":1669912110000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":4,"title":["Dissipative solitons stabilized by nonlinear gradient terms: Time-dependent behavior and generic properties"],"prefix":"10.1063","volume":"32","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3474-0181","authenticated-orcid":false,"given":"Orazio","family":"Descalzi","sequence":"first","affiliation":[{"name":"Complex Systems Group, Facultad de Ingenier\u00eda y Ciencias Aplicadas, Universidad de los Andes 1 , Av. Mons. \u00c1lvaro del Portillo 12.455, Las Condes, Santiago, Chile"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6603-7928","authenticated-orcid":false,"given":"M. I.","family":"Carvalho","sequence":"additional","affiliation":[{"name":"DEEC\/FEUP and INESC TEC. Universidade do Porto 2 , Rua Dr. Roberto Frias, 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2417-6743","authenticated-orcid":false,"given":"M.","family":"Fac\u00e3o","sequence":"additional","affiliation":[{"name":"Departamento de F\u00edsica, Universidade de Aveiro and I3N Campus Universit\u00e1rio de Santiago 3 , 3810-193 Aveiro, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0459-4865","authenticated-orcid":false,"given":"Helmut R.","family":"Brand","sequence":"additional","affiliation":[{"name":"Department of Physics, University of Bayreuth 4 , 95440 Bayreuth, Germany"}]}],"member":"317","published-online":{"date-parts":[[2022,12,1]]},"reference":[{"key":"2024031600290929800_c1","doi-asserted-by":"publisher","first-page":"2761","DOI":"10.1103\/PhysRevA.35.2761","volume":"35","year":"1987","journal-title":"Phys. Rev. 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