Abstract
The authors show the disintegration of a higher-order rogue wave solution of the nonlinear Schr\odinger equation into its constituent parts in the presence of system perturbation.
Highlights
The discovery of the soliton solutions for certain types of nonlinear evolution equations marks an important milestone in mathematical physics
nonlinear Schrödinger equation (NLSE) and its solutions have been applied in optics, plasma physics, hydrodynamics, condensed matter physics, and Bose-Einstein condensates [1,2,3,4], while in mathematics they are studied in integrability, Riemann-Hilbert problems, as well as in the theory of solitons and rogue waves [5,6]
The successful implementation of the inverse scattering transformation on NLSE by Zakharov and Shabat led to the soliton solutions in their exact mathematical forms [7]
Summary
The discovery of the soliton solutions for certain types of nonlinear evolution equations marks an important milestone in mathematical physics. In the Fourier domain, this translates to generating a cascade of spectral sidebands These sidebands and the original continuous-wave exchange energy, eventually forming a series of pulses which gives rise to the Akhmediev breather solution [14]. This breather solution appears in the form of well-known rogue wave solution as its limiting case when the period in the transverse dimension becomes infinite. We demonstrate that under weak symmetry-breaking perturbation, a higher-order rogue wave solution breaks apart and reduces to its constituent fundamental rogue waves. This fascinating observation bears a striking similarity to soliton fission phenomena. Its amplitude and phase profiles at the maximum compression point are shown in Figs. 1(c) and 1(d)
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