Breather Solutions to a Two-dimensional Nonlinear Schrödinger Equation with Non-local Derivatives

2022/09/16 by Alexander Hrabski, Yulin Pan, Hrabski, Alexander +1
Physics and Astronomy · #Advanced Fiber Laser Technologies #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Nonlinear Photonic Systems #Pattern Formation and Solitons (nlin.PS)

paper · pdf · doi:10.48550/arxiv.2209.08155

openalex publication_date 2022/09/16 · openalex created_date 2022/09/21 · openalex updated_date 2026/07/28

Abstract

We consider the nonlinear Schrödinger equation with non-local derivatives in a two-dimensional periodic domain. For certain orders of derivatives, we find a new type of breather solution dominating the field evolution at low nonlinearity levels. With the increase of nonlinearity, the breathers break down, giving way to wave turbulence (or Rayleigh-Jeans) spectra. Phase-space trajectories associated with the breather solutions are found to be close to that of the linear system, revealing a connection between the breather solution and Kolmogorov-Arnold-Moser (KAM) theory.

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