Quasi-stationary method in the study of perturbations to the solitonic solutions of the nonlinear Schrödinger equation

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Title Quasi-stationary method in the study of perturbations to the solitonic solutions of the nonlinear Schrödinger equation
Método quasi-estacionario en el estudio de perturbaciones a las soluciones solitónicas de la ecuación no lineal de Schrödinger
Creator Pavón-Torres, O.
Collantes C., Juan Ramón
Agüero Granados, Máximo A.
Description The fundamental ideas of the multi-scale analysis of perturbations, also called quasi-stationary method, for soliton-like solutions are exposed. In this approach the perturbed nonlinear differential equations are linearized by expanding the solutions around the undisturbed solutions. Consequently, the auto-functions of the linearized operator are calculated to obtain the disturbances of the solitonic solution. Moreover, the evolution of non-linear structures contained in the non-linear Schrödinger equation and cubic-fifth nonlinear Schrödinger equation with damping is studied. The solutions show the variation of the soliton parameters due to this effect.
Se exponen las ideas fundamentales del análisis de perturbaciones a multiescalas, también llamado método quasi-estacionario para soluciones tipo solitón. En esta aproximación las ecuaciones diferenciales no lineales perturbadas son linealizadas expandiendo las soluciones alrededor de las soluciones sin perturbar. En consecuencia, se calculan las auto-funciones del operador linealizado para poder obtener las perturbaciones de la solución solitónica. Además, se estudia la evolución de estructuras no lineales contenidas en la ecuación no lineal de Schrödinger y en la ecuación cúbica-quinta no lineal de Schrödinger con amortiguamiento. Las soluciones muestran la variación de los parámetros del solitón debido a este efecto.
Publisher Universidad Autónoma del Estado de México
Date 2021-06-28
Type info:eu-repo/semantics/article
Artículo revisado por pares
Format application/pdf
Identifier https://cienciaergosum.uaemex.mx/article/view/12820
Source CIENCIA ergo-sum; Vol. 28 Núm. 2 (2021): CIENCIA ergo-sum (julio-octubre 2021)
CIENCIA ergo-sum; Vol. 28 Núm. 2 (2021): CIENCIA ergo-sum (julio-octubre 2021)
Language spa
Relation https://cienciaergosum.uaemex.mx/article/view/12820/12216
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