Geodesic
Solutions of the~Ablowitz--Kaup--Newell--Segur hierarchy equations of the~``rogue wave'' type: A~unified approach
Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 2, pp. 191-220

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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.
Mots-clés : rogue wave, Hirota equation
Keywords: freak wave, nonlinear Schrödinger equation, AKNS hierarchy. 
@article{TMF_2016_186_2_a1,
     author = {V. B. Matveev and A. O. Smirnov},
     title = {Solutions of {the~Ablowitz--Kaup--Newell--Segur} hierarchy equations of the~``rogue wave'' type: {A~unified} approach},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {191--220},
     publisher = {mathdoc},
     volume = {186},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_186_2_a1/}
}
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V. B. Matveev; A. O. Smirnov. Solutions of the~Ablowitz--Kaup--Newell--Segur hierarchy equations of the~``rogue wave'' type: A~unified approach. Teoretičeskaâ i matematičeskaâ fizika, Tome 186 (2016) no. 2, pp. 191-220. http://geodesic.mathdoc.fr/item/TMF_2016_186_2_a1/