Soliton-like behaviour in non-integrable systems
| Autor: | Urbashi Satpathi, Raghavendra Nimiwal, Manas Kulkarni, Vishal Vasan |
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| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Integrable system Complex system FOS: Physical sciences General Physics and Astronomy Pattern Formation and Solitons (nlin.PS) Schrödinger equation symbols.namesake Korteweg–de Vries equation Nonlinear Sciences::Pattern Formation and Solitons Fredholm alternative Mathematical Physics Physics Nonlinear Sciences - Exactly Solvable and Integrable Systems Statistical and Nonlinear Physics Mathematical Physics (math-ph) Nonlinear Sciences - Pattern Formation and Solitons Nonlinear system Nonlinear Sciences::Exactly Solvable and Integrable Systems Classical mechanics Quantum Gases (cond-mat.quant-gas) Modeling and Simulation symbols Soliton Exactly Solvable and Integrable Systems (nlin.SI) Condensed Matter - Quantum Gases Reduction (mathematics) Physics - Optics Optics (physics.optics) |
| Zdroj: | Journal of Physics A: Mathematical and Theoretical. 54:425701 |
| ISSN: | 1751-8121 1751-8113 |
| Popis: | We present a general scheme for constructing robust excitations (soliton-like) in non-integrable multicomponent systems. By robust, we mean localised excitations that propagate with almost constant velocity and which interact cleanly with little to no radiation. We achieve this via a reduction of these complex systems to more familiar effective chiral field-theories using perturbation techniques and the Fredholm alternative. As a specific platform, we consider the generalised multicomponent Nonlinear Schr\"{o}dinger Equations (MNLS) with arbitrary interaction coefficients. This non-integrable system reduces to uncoupled Korteweg-de Vries (KdV) equations, one for each sound speed of the system. This reduction then enables us to exploit the multi-soliton solutions of the KdV equation which in turn leads to the construction of soliton-like profiles for the original non-integrable system. We demonstrate that this powerful technique leads to the coherent evolution of excitations with minimal radiative loss in arbitrary non-integrable systems. These constructed coherent objects for non-integrable systems bear remarkably close resemblance to true solitons of integrable models. Although we use the ubiquitous MNLS system as a platform, our findings are a major step forward towards constructing excitations in generic continuum non-integrable systems. Comment: 21 pages, 3 figures |
| Databáze: | OpenAIRE |
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