Broader Universality of Rogue Waves of Infinite Order
arXiv:2112.15140 · doi:10.1016/j.physd.2022.133289
Abstract
We show that the same special solution of the focusing nonlinear Schrödinger equation that has been shown to arise in a certain near-field/large-order limit from soliton and Peregrine-like rogue wave solutions actually arises universally from an arbitrary background solution when subjected to a sequence of iterated Bäcklund transformations.
arXiv comment21 pages
References in corpus (15)
- Multi-soliton, multi-breather and higher-order rogue wave solutions to the complex short pulse equation
- Universal Peregrine soliton structure in nonlinear pulse compression in optical fiber
- Multi-breathers and high order rogue waves for the nonlinear Schrödinger equation on the elliptic function background
- Extreme Superposition: Rogue Waves of Infinite Order and the Painlevé-III Hierarchy
- The role of multiple soliton and breather interactions in generation of rogue waves: the mKdV framework
- Far-Field Asymptotics for Multiple-Pole Solitons in the Large-Order Limit
- Rogue waves in the generalized derivative nonlinear Schrodinger equations
- Large-order asymptotics for multiple-pole solitons of the focusing nonlinear Schrödinger equation
- Universal rogue wave patterns associated with the Yablonskii-Vorob'ev polynomial hierarchy
- Rogue waves on the background of periodic standing waves in the derivative NLS equation
- Theoretical and experimental evidence of non-symmetric doubly localized rogue waves
- The height of an th-order fundamental rogue wave for the nonlinear Schrödinger equation
- Influence of small dispersion on self-focusing in spatially one-dimensional case
- Rogue waves of Ultra-High Peak Amplitude: A Mechanism for Reaching up to Thousand Times the Background Level
- Extreme Superposition: High-Order Fundamental Rogue Waves in the Far-Field Regime