2020/07/03 by Amin Chabchoub, Takuji Waseda, Chabchoub, Amin +7
Earth and Planetary Sciences · #Coastal and Marine Dynamics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Ocean Waves and Remote Sensing #Oceanographic and Atmospheric Processes #Pattern Formation and Solitons (nlin.PS)
paper · pdf · doi:10.48550/arxiv.2007.01956
openalex publication_date 2020/07/03 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Soliton and breather solutions of the nonlinear Schr "odinger equation (NLSE)\nare known to model localized structures in nonlinear dispersive media such as\non the water surface. One of the conditions for an accurate propagation of such\nexact solutions is the proper generation of the exact initial phase-shift\nprofile in the carrier wave, as defined by the NLSE envelope at a specific time\nor location. Here, we show experimentally the significance of such initial\nexact phase excitation during the hydrodynamic propagation of localized\nenvelope solitons and breathers, which modulate a plane wave of constant\namplitude (finite background). Using the example of stationary black solitons\nin intermediate water depth and pulsating Peregrine breathers in deep-water, we\nshow how these localized envelopes disintegrate while they evolve over a long\npropagation distance when the initial phase shift is zero. By setting the\nenvelope phases to zero, the dark solitons will disintegrate into two gray-type\nsolitons and dispersive elements. In the case of the doubly-localized Peregrine\nbreather the maximal amplification is considerably retarded; however locally,\nthe shape of the maximal focused wave measured together with the respective\nsignature phase-shift are almost identical to the exact analytical Peregrine\ncharacterization at its maximal compression location. The experiments,\nconducted in two large-scaled shallow-water as well as deep-water wave\nfacilities, are in very good agreement with NLSE simulations for all cases.\n