Continuous families of solitary waves in non-symmetric complex potentials: A Melnikov theory approach
The existence of stationary solitary waves in symmetric and non-symmetric complex potentials is studied by means of Melnikov’s perturbation method. The latter provides analytical conditions for the existence of such waves that bifurcate from the homogeneous nonlinear modes of the system and are loca...
| Autores: | , , , , |
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| Formato: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2019 |
| País: | España |
| Recursos: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/81732 |
| Acesso em linha: | https://hdl.handle.net/11441/81732 https://doi.org/10.1016/j.chaos.2018.11.021 |
| Access Level: | acceso abierto |
| Palavra-chave: | Solitary waves Complex potentials Symmetry breaking PT-symmetry Melnikov’s method Homoclinic bifurcations |
| Resumo: | The existence of stationary solitary waves in symmetric and non-symmetric complex potentials is studied by means of Melnikov’s perturbation method. The latter provides analytical conditions for the existence of such waves that bifurcate from the homogeneous nonlinear modes of the system and are located at specific positions with respect to the underlying potential. It is shown that the necessary conditions for the existence of continuous families of stationary solitary waves, as they arise from Melnikov theory, provide general constraints for the real and imaginary part of the potential, that are not restricted to symmetry conditions or specific types of potentials. Direct simulations are used to compare numerical results with the analytical predictions, as well as to investigate the propagation dynamics of the solitary waves. |
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