AI Article Synopsis
- This text discusses the derivation of super-regular (SR) breather solutions in systems with self-steepening effects, using a mathematical approach called the Darboux transformation.
- Unlike traditional SR breather solutions that remain symmetric, the new solutions evolve asymmetrically even when they start from symmetric conditions, highlighting unique dynamic behaviors.
- Numerical simulations validate the existence of these new SR breathers, suggesting potential experimental observations in various systems such as optical frequency-doubling crystals and magnetized plasmas.
Article Abstract
A family of super-regular (SR) breather solutions in systems with self-steepening effect and in the case of either normal or anomalous dispersion is derived analytically. Derivation is based on the Darboux transformation with a quadratic spectral parameter. In contrast to the SR breather solutions in t-symmetric systems such as the nonlinear Schrödinger equation, the new breathers found in the present work evolve asymmetrically even if started from symmetric initial conditions. The initial stage of this process is modulation instability. Numerical simulations confirm the excitation of the SR breathers when started from the approximate initial conditions leading at first to modulation instability. Our results offer the possibility of experimental observations of SR breather dynamics in systems with self-steepening effects, such as optical frequency-doubling crystals or magnetized plasmas.
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| http://dx.doi.org/10.1103/PhysRevE.100.062201 | DOI Listing |
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