Rogue wave patterns in the nonlinear Schrödinger equation
arXiv:2101.00383
Abstract
Rogue wave patterns in the nonlinear Schrödinger equation are analytically studied. It is shown that when an internal parameter in the rogue waves (which controls the shape of initial weak perturbations to the uniform background) is large, these waves would exhibit clear geometric structures, which are formed by Peregrine waves in shapes such as triangle, pentagon, heptagon and nonagon, with a possible lower-order rogue wave at its center. These rogue patterns are analytically determined by the root structures of the Yablonskii-Vorob'ev polynomial hierarchy, and their orientations are controlled by the phase of the large parameter. It is also shown that when multiple internal parameters in the rogue waves are large but satisfy certain constraints, similar rogue patterns would still hold. Comparison between true rogue patterns and our analytical predictions shows excellent agreement.
arXiv comment21 pages, 7 figures
References in corpus (11)
- Nonlinear Schrödinger Equation: Generalized Darboux Transformation and Rogue Wave Solutions
- Deterministic Vector Freak Waves
- General high-order rogue waves and their dynamics in the nonlinear Schroedinger equation
- Vector Rogue Waves and Baseband Modulation Instability in the Defocusing Regime
- A generating mechanism for higher order rogue waves
- Rogue waves emerging from the resonant interaction of three waves
- High-order Rogue Waves in Vector Nonlinear Schrödinger Equations
- Rational solitons of wave resonant interaction models
- Observation of a Group of Dark Rogue Waves in a Telecommunication Optical Fiber
- Determinant Structure of the Rational Solutions for the Painlevé II Equation
- Universal patterns of rogue waves