{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T12:56:53Z","timestamp":1791550613477,"version":"4.3.4"},"reference-count":43,"publisher":"AIP Publishing","issue":"7","license":[{"start":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T00:00:00Z","timestamp":1690416000000},"content-version":"vor","delay-in-days":26,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T00:00:00Z","timestamp":1690416000000},"content-version":"tdm","delay-in-days":26,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100024023","name":"Korea Institute for Advanced Study","doi-asserted-by":"publisher","award":["CG086101"],"award-info":[{"award-number":["CG086101"]}],"id":[{"id":"10.13039\/501100024023","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2023,7,1]]},"abstract":"<jats:p>We study different types of solitons of a generalized nonlinear Schr\u00f6dinger equation (GNLSE) that models optical pulses traveling down an optical waveguide with quadratic as well as quartic dispersion. A traveling-wave ansatz transforms this partial differential equation into a fourth-order nonlinear ordinary differential equation (ODE) that is Hamiltonian and has two reversible symmetries. Homoclinic orbits of the ODE that connect the origin to itself represent solitons of the GNLSE, and this allows one to study the existence and organization of solitons with advanced numerical tools for the detection and continuation of connecting orbits. In this paper, we establish the existence of new types of connecting orbits, namely, PtoP connections from one periodic orbit to another. As we show, these global objects provide a general mechanism that generates additional families of two types of solitons in the GNLSE. First, we find generalized solitons with oscillating tails whose amplitude does not decay but reaches a nonzero limit. Second, PtoP connections in the zero energy level can be combined with EtoP connections from the origin to a selected periodic orbit to create multi-oscillation solitons; their characterizing property is to feature several episodes of different oscillations in between decaying tails. As is the case for solitons that were known previously, generalized solitons and multi-oscillation solitons are shown to be an integral part of the phenomenon of truncated homoclinic snaking.<\/jats:p>","DOI":"10.1063\/5.0152562","type":"journal-article","created":{"date-parts":[[2023,7,27]],"date-time":"2023-07-27T15:07:15Z","timestamp":1690470435000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":11,"title":["Generalized and multi-oscillation solitons in the nonlinear Schr\u00f6dinger equation with quartic dispersion"],"prefix":"10.1063","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5701-3174","authenticated-orcid":false,"given":"Ravindra","family":"Bandara","sequence":"first","affiliation":[{"name":"Department of Mathematics and Dodd-Walls Centre for Photonic and Quantum Technologies, The University of Auckland 1 , Private Bag 92019, Auckland 1142, New Zealand"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6742-775X","authenticated-orcid":false,"given":"Andrus","family":"Giraldo","sequence":"additional","affiliation":[{"name":"School of Computational Sciences, Korea Institute for Advanced Studies 2 , Seoul 02455, South Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Neil G. R.","family":"Broderick","sequence":"additional","affiliation":[{"name":"Department of Physics and Dodd-Walls Centre for Photonic and Quantum Technologies, The University of Auckland 3 , Private Bag 92019, Auckland 1142, New Zealand"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8940-230X","authenticated-orcid":false,"given":"Bernd","family":"Krauskopf","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Dodd-Walls Centre for Photonic and Quantum Technologies, The University of Auckland 1 , Private Bag 92019, Auckland 1142, New Zealand"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2023,7,27]]},"reference":[{"key":"2023072719052836900_c1","doi-asserted-by":"publisher","first-page":"025801","DOI":"10.1103\/PhysRevA.87.025801","article-title":"Formation of quartic solitons and a localized continuum in silicon-based slot waveguides","volume":"87","year":"2013","journal-title":"Phys. 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