6533b82efe1ef96bd12929d1
RESEARCH PRODUCT
AKNS and NLS hierarchies, MRW solutions, $P_n$ breathers, and beyond
A. O. SmirnovVladimir Borisovich MatveevVladimir Borisovich Matveevsubject
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 physicsdescription
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-3 quasi-rational solutions that can be used for prediction and modeling of the rogue wave events in fiber optics, hydrodynamics, and many other branches of science.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-3 quasi-rational solutions that can be used for prediction and modeling of the rogue wave events in fiber optics, hydrodynamics, and many other branches of science.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-09-01 |