Universal rogue wave patterns associated with the Yablonskii-Vorob'ev polynomial hierarchy

Abstract

We show that universal rogue wave patterns exist in integrable systems. These rogue patterns comprise fundamental rogue waves arranged in shapes such as triangle, pentagon and heptagon, with a possible lower-order rogue wave at the center. These patterns appear when one of the internal parameters in bilinear expressions of rogue waves gets large. Analytically, these patterns are determined by the root structures of the Yablonskii-Vorob'ev polynomial hierarchy through a linear transformation. Thus, the induced rogue patterns in the space-time plane are simply the root structures of Yablonskii-Vorob'ev polynomials under actions such as dilation, rotation, stretch, shear and translation. As examples, these universal rogue patterns are explicitly determined and graphically illustrated for the generalized derivative nonlinear Schrödinger equations, the Boussinesq equation, and the Manakov system. Similarities and differences between these rogue patterns and those reported earlier in the nonlinear Schrödinger equation are discussed.

arXiv comment30 pages,8 figures,2 tables

References in corpus (20)

• 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
• A generating mechanism for higher order rogue waves
• Vector Rogue Waves and Baseband Modulation Instability in the Defocusing Regime
• The Darboux transformation of the derivative nonlinear Schrödinger equation
• High Order Solutions and Generalized Darboux Transformations of Derivative Schrödinger Equation
• Rogue waves emerging from the resonant interaction of three waves
• High-order Rogue Waves in Vector Nonlinear Schrödinger Equations
• Dark-dark solitons and modulational instability in miscible, two-component Bose-Einstein condensates
• Rational solitons of wave resonant interaction models
• Bilinearization of a Generalized Derivative Nonlinear Schrödinger equation
• General rogue waves in the focusing and defocusing Ablowitz-Ladik equations
• Observation of a Group of Dark Rogue Waves in a Telecommunication Optical Fiber
• Determinant Structure of the Rational Solutions for the Painlevé II Equation
• Rogue waves in the generalized derivative nonlinear Schrodinger equations
• High-order Rogue Wave solutions for the Coupled Nonlinear Schrödinger Equations-II
• General high-order rogue waves of the (1+1)-dimensional Yajima-Oikawa system
• General rogue waves in the Boussinesq equation
• High-order rogue waves of a long wave-short wave model

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