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Integrable nonlocal Hirota equations

Fring, A. ORCID: 0000-0002-7896-7161, Correa, F. & Cen, J. (2019). Integrable nonlocal Hirota equations. Journal of Mathematical Physics, 60, 81508. doi: 10.1063/1.5013154


We construct several new integrable systems corresponding to nonlocal ver-sions of the Hirota equation, which is a particular example of higher order nonlinearSchrödinger equations. The integrability of the new models is established by providingtheir explicit forms of Lax pairs or zero curvature conditions.The two compatibility equa-tions arising in this construction are found to be related to each other either by a paritytransformationP, by a time reversalTor aPT-transformation possibly combined with aconjugation. We construct explicit multi-soliton solutions forthese models by employingHirota’s direct method as well as Darboux-Crum transformations.The nonlocal natureof these models allows for a modification of these solution procedures as the new systemsalso possess new types of solutions with different parameter dependence and differentqualitative behaviour. The multi-soliton solutions are of varied type, being for instancenonlocal in space, nonlocal in time of time crystal type, regular with local structureseither in time/space or of rogues wave type.

Publication Type: Article
Additional Information: This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article, Fring, A., Correa, F., and Cen, J. (2019). Integrable nonlocal Hirota equations, appeared in Journal of Mathematical Physics, 60, 081508 and may be found at
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Mathematics
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