0000000000726867

AUTHOR

A. O. Smirnov

showing 2 related works from this author

AKNS and NLS hierarchies, MRW solutions, $P_n$ breathers, and beyond

2018

We describe a unified structure of rogue wave and multiple rogue wave solutions for all equations of the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy and their mixed and deformed versions. The definition of the AKNS hierarchy and its deformed versions is given in the Sec. II. We also consider the continuous symmetries of the related equations and the related spectral curves. This work continues and summarises some of our previous studies dedicated to the rogue wave-like solutions associated with AKNS, nonlinear Schrodinger, and KP hierarchies. The general scheme is illustrated by the examples of small rank n, n ⩽ 7, rational or quasi-rational solutions. In particular, we consider rank-2 and …

Rank (linear algebra)BreatherStructure (category theory)Statistical and Nonlinear PhysicsWave equation01 natural sciences010305 fluids & plasmasNonlinear systemsymbols.namesakeNonlinear Sciences::Exactly Solvable and Integrable Systems[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]0103 physical sciencesHomogeneous spacesymbolsRogue wave010306 general physicsNonlinear Sciences::Pattern Formation and SolitonsMathematical PhysicsSchrödinger's catMathematicsMathematical physics
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Многофазные решения нелокальных симметричных редукций уравнений иерархии АКНС: общий анализ и простейшие примеры

2020

Рассмотрены нелокальные симметрии, которыми обладают все или все четные (все нечетные) уравнения из иерархии АКНС. Построены примеры решений, удовлетворяющих одновременно нескольким нелокальным уравнениям из иерархии АКНС. Проведено подробное исследование однофазных решений.

0103 physical sciences010306 general physics01 natural sciences010305 fluids & plasmasTeoreticheskaya i Matematicheskaya Fizika
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