Solitones no autónomos de la ecuación no lineal de Schrödinger con potencial lineal
Article Sidebar
Publicado
oct 6, 2025
##plugins.pubIds.doi.readerDisplayName##
https://doi.org/10.30878/ces.v33n0a50
Main Article Content
Felix Enrique Mendez Zuñiga
http://orcid.org/0009-0007-7994-5005
Maximo Augusto Agüero Granados
http://orcid.org/0000-0002-9861-8997
Tatyana Leonidovna Belyaeva
http://orcid.org/0000-0002-6960-3841
http://orcid.org/0009-0007-7994-5005
Maximo Augusto Agüero Granados
http://orcid.org/0000-0002-9861-8997
Tatyana Leonidovna Belyaeva
http://orcid.org/0000-0002-6960-3841
Resumen
En este trabajo nosotros investigamos la ecuación no lineal de Schrödinger con potencial lineal. Para el estudio se utiliza el método propuesto por M. Ablowitz, D. Kaup, A. Newell, y H. Segur con el objetivo de obtener la integrabilidad de la ecuación mencionada y la transformada de Bäcklund para soluciones solitónicas. Analizamos la dinámica de un solitón y demostramos la existencia de interacción elástica de solitones no autónomos.
Article Details
Como citar
MENDEZ ZUÑIGA, Felix Enrique; AGÜERO GRANADOS, Maximo Augusto; BELYAEVA, Tatyana Leonidovna.
Solitones no autónomos de la ecuación no lineal de Schrödinger con potencial lineal.
CIENCIA ergo-sum, [S.l.], v. 33, oct. 2025.
ISSN 2395-8782.
Disponible en: <https://cienciaergosum.uaemex.mx/article/view/24297>. Fecha de acceso: 13 feb. 2026
doi: https://doi.org/10.30878/ces.v33n0a50.
Sección
Ciencias exactas y aplicadas
Esta obra está bajo licencia internacional Creative Commons Reconocimiento-NoComercial-SinObrasDerivadas 4.0.
Citas
Ablowitz, M., & Segur, H. (1981). Solitons and the Inverse Scattering Transform. Philadelphia, PA: SIAM.
Ablowitz, M. J., Kaup, D. J., Newell, A. C., & Segur, H. (1973). Nonlinear-Evolution Equations of Physical Significance. Physical Review Letters, 31, 125.
Agrawal, G. P. (2001). Nonlinear Fiber Optics (3rd ed.). San Diego, CA: Academic Press.
Agüero Granados, M. A., & Serkin, V. N. (2020). Introducción a la teoría de solitones. Ediciones y Gráficos Eón, S.A. de C.V.
Belyaeva, T. L., & Serkin, V. N. (2011). Nonautonomous Solitons: Applications from Nonlinear Optics to BEC and Hydrodynamics. In Hydrodynamics – Advanced Topics.
Chen, H. H. (1974). General Derivation of Bäcklund Transformations from Inverse Scattering Problems. Physical Review Letters, 33, 925.
Chen, H. H., & Liu, C. S. (1976). Solitons in nonuniform media. Physical Review Letters, 37, 693.
Gardner, C. S., Greene, J. M., Kruskal, M. D., & Miura, R. M. (1967). Method for solving the Korteweg-de Vries equation. Physical Review Letters, 19, 1095.
Hasegawa, A., & Kodama, Y. (1995). Solitons in Optical Communications. New York, NY: Oxford University Press.
Mendez-Zuñiga, I.M., T.L. Belyaeva, M.A. Agüero, V.N. Serkin (2023). Emergence of polynomial external potentials in solitonic hierarchies: Applications to the nonisospectral LPDE model. Optik - International Journal for Light and Electron Optics, Optik Volume 287, September 2023, 170904
Lax, P. D. (1968). Integrals of nonlinear equations of evolution and solitary waves. Communications on Pure and Applied Mathematics, 21, 467.
Rangwala, A. A., & Rao, J. A. (1985). Complete soliton solutions of the ZS / AKNS equations of the Inverse Scattering Method. Physical Review Letters, 112A, 188.
Serkin, V. N., & Hasegawa, A. (2000). Novel soliton solutions of the nonlinear Schrödinger equation model. Physical Review Letters, 85, 4502.
Serkin, V. N., Hasegawa, A., & Belyaeva, T. L. (2007). Nonautonomous solitons in external potentials. Physical Review Letters, 98, 074102.
Serkin, V. N., Hasegawa, A., & Belyaeva, T. L. (2010). Solitary waves in nonautonomous nonlinear and dispersive systems: nonautonomous solitons. Journal of Modern Optics, 57, 1456–1472.
Taylor, J. R. (1992). Optical Solitons—Theory and Experiment. Cambridge, UK: Cambridge University Press.
T.L. Belyaeva, M.A. Agüero, V.N. Serkin. (2021). Nonautonomous solitons of the novel nonlinear Schrödinger equation: Self-compression, amplification, and the bound state decay in external potentials. Optik - International Journal for Light and Electron Optics, Optik Volume 244, October 2021, 167584.
Ablowitz, M. J., Kaup, D. J., Newell, A. C., & Segur, H. (1973). Nonlinear-Evolution Equations of Physical Significance. Physical Review Letters, 31, 125.
Agrawal, G. P. (2001). Nonlinear Fiber Optics (3rd ed.). San Diego, CA: Academic Press.
Agüero Granados, M. A., & Serkin, V. N. (2020). Introducción a la teoría de solitones. Ediciones y Gráficos Eón, S.A. de C.V.
Belyaeva, T. L., & Serkin, V. N. (2011). Nonautonomous Solitons: Applications from Nonlinear Optics to BEC and Hydrodynamics. In Hydrodynamics – Advanced Topics.
Chen, H. H. (1974). General Derivation of Bäcklund Transformations from Inverse Scattering Problems. Physical Review Letters, 33, 925.
Chen, H. H., & Liu, C. S. (1976). Solitons in nonuniform media. Physical Review Letters, 37, 693.
Gardner, C. S., Greene, J. M., Kruskal, M. D., & Miura, R. M. (1967). Method for solving the Korteweg-de Vries equation. Physical Review Letters, 19, 1095.
Hasegawa, A., & Kodama, Y. (1995). Solitons in Optical Communications. New York, NY: Oxford University Press.
Mendez-Zuñiga, I.M., T.L. Belyaeva, M.A. Agüero, V.N. Serkin (2023). Emergence of polynomial external potentials in solitonic hierarchies: Applications to the nonisospectral LPDE model. Optik - International Journal for Light and Electron Optics, Optik Volume 287, September 2023, 170904
Lax, P. D. (1968). Integrals of nonlinear equations of evolution and solitary waves. Communications on Pure and Applied Mathematics, 21, 467.
Rangwala, A. A., & Rao, J. A. (1985). Complete soliton solutions of the ZS / AKNS equations of the Inverse Scattering Method. Physical Review Letters, 112A, 188.
Serkin, V. N., & Hasegawa, A. (2000). Novel soliton solutions of the nonlinear Schrödinger equation model. Physical Review Letters, 85, 4502.
Serkin, V. N., Hasegawa, A., & Belyaeva, T. L. (2007). Nonautonomous solitons in external potentials. Physical Review Letters, 98, 074102.
Serkin, V. N., Hasegawa, A., & Belyaeva, T. L. (2010). Solitary waves in nonautonomous nonlinear and dispersive systems: nonautonomous solitons. Journal of Modern Optics, 57, 1456–1472.
Taylor, J. R. (1992). Optical Solitons—Theory and Experiment. Cambridge, UK: Cambridge University Press.
T.L. Belyaeva, M.A. Agüero, V.N. Serkin. (2021). Nonautonomous solitons of the novel nonlinear Schrödinger equation: Self-compression, amplification, and the bound state decay in external potentials. Optik - International Journal for Light and Electron Optics, Optik Volume 244, October 2021, 167584.