Adiabatic approach for the interaction of two solitones with gain and losses

CIENCIA ergo-sum

View Publication Info
 
 
Field Value
 
Title Adiabatic approach for the interaction of two solitones with gain and losses
Aproximación adiabática para la interacción de dos solitones con ganancias y pérdidas
 
Creator Maguiña Palma, Misael Erikson
Agüero Granados, Máximo Augusto
Leonidovna Belyaeva, Tatyana
Serkin Nikolaevich, Vladimir
 
Description The interaction of soliton solutions of the Nonlinear Schrödinger Equation is studied based on the adiabatic approach for the system parameters. The dynamics of two solitons with gain and loss in amplification is analyzed. If the perturbation is not present, the in-phase soliton interaction is attractive and forms a bound state. While the solitons are in phase with gain in amplification, their amplitudes increase; but the period of oscillation of the bound state and the relative distance between the solitons decrease. For the case of loss in amplification, the amplitude decreases and the solitons begin to repel, consequently, the period of oscillations and the relative distance between solitons increase. 
Se estudia la interacción de solitones de la ecuación diferencial no lineal de Schördinger basada en la aproximación adiabática para los parámetros del sistema. Se analiza la dinámica de dos solitones con ganancia y pérdida en amplificación. Si la perturbación no está presente, la interacción de solitones en fase es atractiva y forma un estado ligado. Si los solitones están en fase con ganancia en amplificación, la amplitud crece, pero el periodo de oscilación del estado ligado y la distancia relativa entre los solitones disminuye. Para el caso de pérdida en amplificación, la amplitud decrece y los solitones comienzan a repelerse y por consiguiente, el periodo de oscilaciones y la distancia relativa entre solitones se incrementan. 
 
Publisher Universidad Autónoma del Estado de México
 
Date 2020-06-24
 
Type info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
 
Format application/pdf
text/html
application/zip
 
Identifier https://cienciaergosum.uaemex.mx/article/view/12465
10.30878/ces.v27n4a1
 
Source CIENCIA ergo-sum; Vol. 27 Núm. 4 (2020): Número especial "Retos de la física no lineal"
CIENCIA ergo-sum; Vol. 27 Núm. 4 (2020): Número especial "Retos de la física no lineal"
2395-8782
1405-0269
 
Language spa
 
Relation https://cienciaergosum.uaemex.mx/article/view/12465/11109
https://cienciaergosum.uaemex.mx/article/view/12465/11130
https://cienciaergosum.uaemex.mx/article/view/12465/11131
/*ref*/Agrawal, G. (1989). Nonlinear Fiber Optics. San Diego: Academic Press.
/*ref*/Anderson, D., & M. Lisak. (1986). Bandwidth limits due to mutual pulse interaction in optical soliton communication systems. Opt. Lett., 11, 174-176.
/*ref*/Biswas, A., Milovic, D., & Edwards, M. (2010). Mathematical theory of dispersion-managed optical solitons. Berlin: Springer Science & Business Media.
/*ref*/Bullough, R., & Caudrey, P. J. (1980). Solitons. Berlin: Springer-Verlag.
/*ref*/Christiansen, P. L., Sorensen, M. P., & Scott, A. C. (2000). Nonlinear science at the dawn of the 21st century. Berlin: Springer.
/*ref*/Fujioka, J. (2003). NLS: una introducción ecuación lineal de Schrödinger. México: UNAM.
/*ref*/Gordon, J. (1983). Interaction forces among solitons in optical fibers. Opt. Lett., 8, 596-598.
/*ref*/Hasegawa, A., & Kodama, Y. (1995). Solitons in optical communications. London: Oxford University Press.
/*ref*/Hernandez Tenorio, C., Villagrán Vargas, E., Serkin, V. N., Agüero Granados, T. L., Belyaeva, R., Peña Moreno, R., & Morales Lara, L. (2005). Dynamics of solitons in the model of nonlinear Schrödinger equation with an external harmonic potential: I. Bright solitons. Kvantovaya Elektronica, 35(9), 778-786.
/*ref*/Karpman, V. I., & Solov’ev, V. V. (1981). A perturbation approach to the two soliton system. Physica 3D, 487-502.
/*ref*/Karpman, V., & Maslov, E. (1977). Perturbation theory for solitons. Sov. Phys. JETP, 46(2), 291.
/*ref*/Maguiña-Palma, M., Belyaeva, T., Agüero, M., García-Santibañez, F., & Serkin., V. (2019). Application of Karpman-Maslov-Solov’ev soliton perturbation theory. Optik, 99-104.
/*ref*/Peyrard, M., & Bishop, A. R. (1989). Statistical mechanics of a nonlinear model for DNA. Phys. Rev. Lett., 62, 2755-2758.
/*ref*/Serkin, V. N., Hasegawa, A., & Belyaeva, T. L. (2007). Nonautonomous solitons in external potentials. Phys. Rev. Lett, 98, 074102(1- 4).
/*ref*/Serkin, V., & Hasegawa, A. (2002). Exactly integrable nonlinear Schrödinger equation models with varying dispersion, nonlinearity and gain application for soliton dispersion. IEEE J. Select. Topics Quant. Electron, 418-431.
/*ref*/Serkin, V., & Hasegawa, A. (2000). Soliton management in the nonlinear Schrödinger equation model with varying dispersion, nonlinearity, and gain. JETP Lett., 72, 125-129.
/*ref*/Taylor, J. (1992). Optical solitons-Theory and experiment. Cambridge: Cambridge University Press.
/*ref*/Yang, J. (2010). Nonlinear waves in integrable and nonintegrable systems. Philadelphia: Society for Industrial and Applied Mathematics.
/*ref*/Zakharov, V., & Shabat, A. (1972 ). Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP, 34, 62-69.
 
Rights Derechos de autor 2020 CIENCIA ergo-sum
 

Contact Us

The PKP Index is an initiative of the Public Knowledge Project.

For PKP Publishing Services please use the PKP|PS contact form.

For support with PKP software we encourage users to consult our wiki for documentation and search our support forums.

For any other correspondence feel free to contact us using the PKP contact form.

Find Us

Twitter

Copyright © 2015-2018 Simon Fraser University Library