Método quasi-estacionario en el estudio de perturbaciones a las soluciones solitónicas de la ecuación no lineal de Schrödinger

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O. Pavón-Torres http://orcid.org/0000-0001-8598-6734
Juan Ramón Collantes C. http://orcid.org/0000-0002-6161-9785
Máximo A. Agüero Granados http://orcid.org/0000-0002-9861-8997

Resumen

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.

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PAVÓN-TORRES, O.; COLLANTES C., Juan Ramón; AGÜERO GRANADOS, Máximo A.. Método quasi-estacionario en el estudio de perturbaciones a las soluciones solitónicas de la ecuación no lineal de Schrödinger. CIENCIA ergo-sum, [S.l.], v. 28, n. 2, jun. 2021. ISSN 2395-8782. Disponible en: <https://cienciaergosum.uaemex.mx/article/view/12820>. Fecha de acceso: 25 sep. 2021 doi: https://doi.org/10.30878/ces.v28n2a8.
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Ciencias exactas y aplicadas

Citas

Abdullaev, F., Gammal, A., Tomio, L., & Frederic, T. (2001). Stability of trapped Bose-Einstein condensates. Physical Review A, 63, 043604.

Agüero, M., Belyaeva, T., & Serkin, V. (2011). Compacton anti-compacton pair for hydrogen bonds and rotatiownal waves in DNA dynamics. Communications in Nonlinear Science and Numerical Simulation, 16, 3071-3080.

Belmonte-Beitia, J., & Cuevas, J. (2009). The Journal of Physics A: Mathematical and Theoretical, 42, 165201.
Biswas, A. (2003). Quasi-stationary optical solitons with parabolic law nonlinearity. Optics Communications, 216, 427-437.

Burger, S., Bongs, K., Dettmer, S., Ertmer, W., & Sengstock, K. (1999). Dark solitons in Bose-Einstein condensates. Physical Review Letters, 83, 5198-5201.

Craik, A. (1985). Wave interactions and fluid flows. London: Cambridge University Press.

Cuenda, S., Sánchez, A., T., & Quintero, Niurka R. (2006). Does the dynamics of sine-Gordon solitons predict active regions of DNA. Physica D: Nonlinear Phenomena, 223, 214-221.

Daniel, M., & Vanitha, M. (2011). Solitons in an inhomogeneous, helical DNA molecular chain with flexible strands. Physical Review E, 84, 031928.

Flesh, R., & Trullinger, S. (1987). Green’s functions for nonlinear Klein-Gordon kink perturbation theory. Journal of Mathematical Physics, 28, 1619-1631.

Gedalin, M., Scott, T., & Band, Y. (1997). Optical solitary waves in the higher order nonlinear Schrödinger equation. Physical Review Letters, 78, 448-451.

Goullet, A., & Choi, W. (2011). A numerical and experimental study on the nonlinear evolution of long-crested irregular waves. Physics of Fluids, 23, 016601.

Hacinliyan, I., & Erbay, S. (2004). Coupled quintic nonlinear Schrödinger equations in a generalized elastic solid. Journal of Physics A: Mathematical and Theoretical, 37, 9387.

Hermann, R. L. (1990). A direct approach to studying soliton perturbations. Journal of Physics A Mathematical and General, 23, 2327-2362.

Karpman, V. I., & Maslow, E. M. (1977). Perturbation theory for solitons. Journal of Experimental and Theoretical Physics, 73, 281-291.

Kartavenko, V. (1984). Soliton-like solutikons in nuclear hydrodynamics. Soviet Journal of Nuclear Physics, 40, 240-246.

Kodoma, Y., & Ablowitz, M. J. (1981). Perturbations of solitons and solitary waves. Studies in Applied Mathematicse, 64, 225-245.

Kumar, A., Sarkar, S., & Ghatak, A. (1986). Effects of fifth order non-linearity in refractive index on Gaussian pulse propagations in lossy optical fibers. Optics Letters, 11, 321-323.

Kurkina, O., Kurkin, A., Soomere, T., & Pelinovsky, E. (2011). Higher-order (2+4) Korteweg-de Vries-like equation for interfacial waves in a symmetric three-layer fluid. Physics of Fluids, 23, 116602.

Pavon-Torres, O., Agüero, M., Belyaeva, T., Ramirez, A., & Serkin, V. (2019). Unusual self-spreading or self-compression of the cubic-quintic NLSE solitons owing to amplification or absorption. Optik, 184, 446-456.

Peng, Y., & Krishnan, E. (2007). New exact solutions for the cubic-quintic nonlinear Schrödinger equation. Communications in Mathematical Sciences, 5, 243-252.

Salerno, M. (1991). Discrete model for DNA-promoter dynamics. Physical Review A, 44, 5292-5297.

Serkin, V., Belyaeva, T., Alexandrov, I., & Melo Melchor, G. (2001). Novel topological quasi-soliton solutions for the nonlinear cubic-quintic Schrödinger equation. Proc. SPIE 4271, Optical Pulse and Beam Propagation III, 292-302.

Torres, O. P., & Granados, M. A. (2016). Exact traveling wave solutions in the coupled plane-base rotator model of DNA. International Journal of Non-Linear Mechanics, 86, 8-14.

Triki, H., & Taha, T. (2012). Solitary wave solutions for a higher order nonlinear Schrödinger equation. Mathematics and Computers in Simulation 2012, 1333-1340.

Vasumathi, V., & Daniel, M. (2009). Base-pair opening and bubble transport in a DNA double helix induced by a protein molecule in a viscous medium. Physical Review E, 80, 061904.

Yan, J., Tang, Y., Zhou, G., & Chen, Z. (1998). Direct approach to the study of soliton perturbations of nonlinear Schrödinger equation and the sine-Gordon. Physical Review E, 58, 1064-1073.

Zayed, E., & Amer, Y. (2017). Many exact solutions for a higher order nonlinear Schrödinger equation with non-kerr terms describing the propagation of femtosecond optical pulses in nonlinear optical fibers. Computational Mathematics and Modeling, 28, 118-139.

Zhou, C., & He, X. (1994). Stochastic diffusion of electrons in evolutive Langmuir fields. Physica Scripta, 50, 415-418.