Numerical spectral synthesis of breather gas for the focusing nonlinear Schrödinger equation

Abstract

We numerically realize breather gas for the focusing nonlinear Schrödinger equation. This is done by building a random ensemble of N $\sim$ 50 breathers via the Darboux transform recursive scheme in high precision arithmetics. Three types of breather gases are synthesized according to the three prototypical spectral configurations corresponding the Akhmediev, Kuznetsov-Ma and Peregrine breathers as elementary quasi-particles of the respective gases. The interaction properties of the constructed breather gases are investigated by propagating through them a "trial" generic breather (Tajiri-Watanabe) and comparing the mean propagation velocity with the predictions of the recently developed spectral kinetic theory (El and Tovbis, PRE 2020).

References in corpus (26)

• Nonlinear Schrödinger Equation: Generalized Darboux Transformation and Rogue Wave Solutions
• Modulation instability, Akhmediev Breathers and continuous wave supercontinuum generation
• General high-order rogue waves and their dynamics in the nonlinear Schroedinger equation
• A generating mechanism for higher order rogue waves
• Dispersive shock waves and modulation theory
• Rogue waves and analogies in optics and oceanography
• On the nonlinear stage of Modulation Instability
• Direct observation of Rogue Waves in optical turbulence using Time Microscopy
• Kinetic equation for a dense soliton gas
• Optical Rogue Waves in integrable turbulence
• Soliton Turbulence in Shallow Water Ocean Surface Waves
• Fast Numerical Nonlinear Fourier Transforms
• Bound state soliton gas dynamics underlying the noise-induced modulational instability
• The thermodynamic limit of the Whitham equations
• Experimental evidence of a hydrodynamic soliton gas
• Nonlinear spectral synthesis of soliton gas in deep-water surface gravity waves
• Strongly interacting soliton gas and formation of rogue waves
• Spectral theory of soliton and breather gases for the focusing nonlinear Schrödinger equation
• Solitonic dispersive hydrodynamics: theory and observation
• Formation of rogue waves from the locally perturbed condensate
• Experimental Evidence of Hydrodynamic Instantons: The Universal Route to Rogue Waves
• Creation and Characterization of Matter-Wave Breathers
• Experimental realization of Fermi-Pasta-Ulam-Tsingou recurrence in a long-haul optical fiber transmission system
• Statistics of the Nonlinear Discrete Spectrum of a Noisy Pulse
• Rogue waves of Ultra-High Peak Amplitude: A Mechanism for Reaching up to Thousand Times the Background Level
• Rogue wave patterns in the nonlinear Schrödinger equation

Cited by in corpus (6)

• Soliton gas in integrable dispersive hydrodynamics
• Generalized hydrodynamics of the KdV soliton gas
• Dispersive hydrodynamics of soliton condensates for the Korteweg-de Vries equation
• 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
• NonlinearSchrodinger: Higher-Order Algorithms and Darboux Transformations for Nonlinear Schrödinger Equations
• The formation of a soliton gas condensate for the focusing Nonlinear Schrödinger equation