Solitones no autónomos de la ecuación no lineal de Schrödinger con potencial lineal Non-Autonomous Solitons of the Nonlinear Schrödinger Equation with Linear Potential
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oct 6, 2025
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https://doi.org/10.30878/ces.v33n0a50
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Felix Enrique Mendez Zuñiga
http://orcid.org/0009-0007-7994-5005
Máximo 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
Máximo Augusto Agüero Granados
http://orcid.org/0000-0002-9861-8997
Tatyana Leonidovna Belyaeva
http://orcid.org/0000-0002-6960-3841
Resumen
Se investiga la ecuación no lineal de Schrödinger con potencial lineal. Para el estudio se utiliza el método que propone 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. Adicionalmente, se analiza la dinámica de un solitón y se demuestra la existencia de interacción elástica de solitones no autónomos.
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Como citar
MENDEZ ZUÑIGA, Felix Enrique; AGÜERO GRANADOS, Máximo 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: 18 ago. 2026
doi: https://doi.org/10.30878/ces.v33n0a50.
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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., y Serkin, V. N. (2020). Introducción a la teoría de solitones. Ediciones y Gráficos Eón,
S.A. de C.V.
Belyaeva, T. L., Agüero, M. A., & Serkin, V. N. (2021). Nonautonomous solitons of the novel nonlinear Schrödinger
equation: Self-compression, amplification, and the bound state decay in external potentials. Optik, 244. https://
doi.org/10.1016/j.ijleo.2021.167584
Belyaeva, T. L., & Serkin, V. N. (2011). Nonautonomous Solitons: Applications from nonlinear optics to BEC
and hydrodynamics. In H. Edmar Schulz, A. L. Andrade Simoes, R. Lobosco (Eds.), Hydrodynamics - Advanced
Topics. https://doi.org/10.5772/26463
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: Oxford University
Press.
Mendez-Zuñiga, I. M., Belyaeva, T. L., Agüero, M. A., Serkin, V. N. (2023). Emergence of polynomial external
potentials in solitonic hierarchies: Applications to the nonisospectral LPDE model. Optik, 287. https://doi.
org/10.1016/j.ijleo.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, 112(5), 188-192.
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: Cambridge University Press.
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., y Serkin, V. N. (2020). Introducción a la teoría de solitones. Ediciones y Gráficos Eón,
S.A. de C.V.
Belyaeva, T. L., Agüero, M. A., & Serkin, V. N. (2021). Nonautonomous solitons of the novel nonlinear Schrödinger
equation: Self-compression, amplification, and the bound state decay in external potentials. Optik, 244. https://
doi.org/10.1016/j.ijleo.2021.167584
Belyaeva, T. L., & Serkin, V. N. (2011). Nonautonomous Solitons: Applications from nonlinear optics to BEC
and hydrodynamics. In H. Edmar Schulz, A. L. Andrade Simoes, R. Lobosco (Eds.), Hydrodynamics - Advanced
Topics. https://doi.org/10.5772/26463
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: Oxford University
Press.
Mendez-Zuñiga, I. M., Belyaeva, T. L., Agüero, M. A., Serkin, V. N. (2023). Emergence of polynomial external
potentials in solitonic hierarchies: Applications to the nonisospectral LPDE model. Optik, 287. https://doi.
org/10.1016/j.ijleo.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, 112(5), 188-192.
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: Cambridge University Press.