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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 186, Number 2, Pages 191–220
DOI: https://doi.org/10.4213/tmf8958 (Mi tmf8958) 		 
This article is cited in 33 scientific papers (total in 33 papers)

Solutions of the Ablowitz–Kaup–Newell–Segur hierarchy equations of the “rogue wave” type: A unified approach

V. B. Matveevab, A. O. Smirnova

a St. Petersburg State University for Aerospace Instrumentation (SUAI), St. Petersburg, Russia
b Institut de Mathématiques de Bourgogne, Université de Bourgogne-Franche Comté, Dijon, France
Full-text PDF (3370 kB) Citations (33)
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DOI: https://doi.org/10.4213/tmf8958
Abstract: We describe a unified structure of solutions for all equations of the Ablowitz–Kaup–Newell–Segur hierarchy and their combinations. We give examples of solutions that satisfy different equations for different parameter values. In particular, we consider a rank-$2$ quasirational solution that can be used to investigate many integrable models in nonlinear optics. An advantage of our approach is the possibility to investigate changes in the behavior of a solution resulting from changing the model.
Keywords: rogue wave, freak wave, nonlinear Schrödinger equation, Hirota equation, AKNS hierarchy.
Received: 28.04.2015
Revised: 31.08.2015
English version:
Theoretical and Mathematical Physics, 2016, Volume 186, Issue 2, Pages 156–182
DOI: https://doi.org/10.1134/S0040577916020033
Bibliographic databases:
MSC: 35Q55; 37C55
Language: Russian
Citation: V. B. Matveev, A. O. Smirnov, “Solutions of the Ablowitz–Kaup–Newell–Segur hierarchy equations of the “rogue wave” type: A unified approach”, TMF, 186:2 (2016), 191–220; Theoret. and Math. Phys., 186:2 (2016), 156–182
Citation in format AMSBIB
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    • This publication is cited in the following 33 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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