Far-Field Asymptotics for Multiple-Pole Solitons in the Large-Order Limit
arXiv:1911.04327 · doi:10.1016/j.jde.2021.06.016
Abstract
The integrable focusing nonlinear Schrodinger equation admits soliton solutions whose associated spectral data consist of a single pair of conjugate poles of arbitrary order. We study families of such multiple-pole solitons generated by Darboux transformations as the pole order tends to infinity. We show that in an appropriate scaling, there are four regions in the space-time plane where solutions display qualitatively distinct behaviors: an exponential-decay region, an algebraic-decay region, a non-oscillatory region, and an oscillatory region. Using the nonlinear steepest-descent method for analyzing Riemann-Hilbert problems, we compute the leading-order asymptotic behavior in the algebraic-decay, non-oscillatory, and oscillatory regions.
Published version of the article. 42 pages, 13 figures
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Cited by in corpus (5)
- Darboux transformation and solitonic solution to the coupled complex short pulse equation
- Soliton shielding of the focusing Nonlinear Schrödinger Equation
- Broader Universality of Rogue Waves of Infinite Order
- Rigorous asymptotic analysis for the Riemann problem of the defocusing nonlinear Schrödinger hydrodynamics
- A new form of general soliton solutions and multiple zeros solutions for a higher-order Kaup-Newell equation