Formation of rogue waves from the locally perturbed condensate

Abstract

The one-dimensional focusing nonlinear Schrodinger equation (NLSE) on an unstable condensate background is the fundamental physical model, that can be applied to study the development of modulation instability (MI) and formation of rogue waves. The complete integrability of the NLSE via inverse scattering transform enables the decomposition of the initial conditions into elementary nonlinear modes: breathers and continuous spectrum waves. The small localized condensate perturbations (SLCP) that grow as a result of MI have been of fundamental interest in nonlinear physics for many years. Here, we demonstrate that Kuznetsov-Ma and superregular NLSE breathers play the key role in the dynamics of a wide class of SLCP. During the nonlinear stage of MI development, collisions of these breathers lead to the formation of rogue waves. We present new scenarios of rogue wave formation for randomly distributed breathers as well as for artificially prepared initial conditions. For the latter case, we present an analytical description based on the exact expressions found for the space-phase shifts that breathers acquire after collisions with each other. Finally, the presence of Kuznetsov-Ma and superregular breathers in arbitrary-type condensate perturbations is demonstrated by solving the Zakharov-Shabat eigenvalue problem with high numerical accuracy.

8 pages, 9 figures. In this version we have extended the work to the breathers of Kuznetsov-Ma. Now the suggested theory covers all known scenarios of the presence of breathers in SLCP

References in corpus (6)

• Direct observation of Rogue Waves in optical turbulence using Time Microscopy
• Optical Rogue Waves in integrable turbulence
• New approaches to coding information using inverse scattering transform
• Rogue waves in multiphase solutions of the focusing NLS equation
• Fermi-Pasta-Ulam recurrence and modulation instability
• The finite gap method and the analytic description of the exact rogue wave recurrence in the periodic NLS Cauchy problem. 1

Cited by in corpus (19)

• Bound state soliton gas dynamics underlying the noise-induced modulational instability
• Rogue waves on the double-periodic background in the focusing nonlinear Schrodinger equation
• Soliton gas in integrable dispersive hydrodynamics
• Strongly interacting soliton gas and formation of rogue waves
• Spectral theory of soliton and breather gases for the focusing nonlinear Schrödinger equation
• Growth rate of modulation instability driven by superregular breathers
• Auto-modulation versus breathers in the nonlinear stage of modulational instability
• The effect of a small loss or gain in the periodic NLS anomalous wave dynamics. I
• The finite gap method and the periodic NLS Cauchy problem of the anomalous waves, for a finite number of unstable modes
• Recent developments in spectral theory of the focusing NLS soliton and breather gases: the thermodynamic limit of average densities, fluxes and certain meromorphic differentials; periodic gases
• Dispersive hydrodynamics of soliton condensates for the Korteweg-de Vries equation
• Chess-Board-Like Spatio-Temporal Interference Patterns and Their Excitation
• Direct scattering transform: catch soliton if you can
• Soliton trapping, transmission and wake in modulationally unstable media
• Numerical spectral synthesis of breather gas for the focusing nonlinear Schrödinger equation
• Vector rogue waves in spin-1 Bose-Einstein condensates with spin-orbit coupling
• Measuring the rogue wave pattern triggered from Gaussian perturbations by deep learning
• On minimal energy solutions to certain classes of integral equations related to soliton gases for integrable systems
• Femtosecond Optical Superregular Breathers