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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.09514 |
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| _version_ | 1866915729797808128 |
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| author | Talukdar, Sagardeep Ramakrishnan, R. Nandy, Sudipta Lakshmanan, M. |
| author_facet | Talukdar, Sagardeep Ramakrishnan, R. Nandy, Sudipta Lakshmanan, M. |
| contents | We present here a study of the bright soliton dynamics in an inhomogeneous fibre by means of variable coefficient Fokas-Lenells equation with time varying dispersion, nonlinearity and gain/loss parameter. At first, we propose our system that governs the propagation of ultrashort pulses in an inhomogeneous fibre. Secondly, under a suitable gauge transformation, we transform the system into a simplified form of variable coefficient Fokas-Lenells equation. The Lax integrability and conservation laws are exhibited. We also study the stability of the generalised plane wave against small amplitude perturbations. Thereafter, by using a nonstandard Hirota bilinearization method with the help of a suitable auxiliary function, we obtain the bright one soliton, two soliton and provide a scheme for obtaining N-bright soliton solutions. The elastic collision dynamics of the two solitons is studied using asymptotic analysis. We also investigate the soliton acceleration/retardation under a suitable choice of dispersion and nonlinearity coefficients. Finally, the dramatic effect of the nonlinear tunnelling of the bright one and two-soliton is also studied under some Gaussian dispersion or nonlinearity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09514 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bright soliton interactions in the variable coefficient Fokas-Lenells equation, Conservation laws, Modulation instability and Soliton tunneling Talukdar, Sagardeep Ramakrishnan, R. Nandy, Sudipta Lakshmanan, M. Pattern Formation and Solitons We present here a study of the bright soliton dynamics in an inhomogeneous fibre by means of variable coefficient Fokas-Lenells equation with time varying dispersion, nonlinearity and gain/loss parameter. At first, we propose our system that governs the propagation of ultrashort pulses in an inhomogeneous fibre. Secondly, under a suitable gauge transformation, we transform the system into a simplified form of variable coefficient Fokas-Lenells equation. The Lax integrability and conservation laws are exhibited. We also study the stability of the generalised plane wave against small amplitude perturbations. Thereafter, by using a nonstandard Hirota bilinearization method with the help of a suitable auxiliary function, we obtain the bright one soliton, two soliton and provide a scheme for obtaining N-bright soliton solutions. The elastic collision dynamics of the two solitons is studied using asymptotic analysis. We also investigate the soliton acceleration/retardation under a suitable choice of dispersion and nonlinearity coefficients. Finally, the dramatic effect of the nonlinear tunnelling of the bright one and two-soliton is also studied under some Gaussian dispersion or nonlinearity. |
| title | Bright soliton interactions in the variable coefficient Fokas-Lenells equation, Conservation laws, Modulation instability and Soliton tunneling |
| topic | Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2601.09514 |