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<p>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 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 generalized plane wave against small amplitude perturbation. Thereafter, by using a nonstandard Hirota bilinearization method with the help of suitable auxiliary function, we obtain the bright one soliton, two soliton and provide a scheme for obtaining <i>N</i>-bright soliton solutions. The elastic collision dynamics of the two solitons is studied using asymptotic analysis. We also investigate the soliton acceleration/retardation under suitable choice of dispersion and nonlinearity coefficients. Finally, the dramatic effect of nonlinear tunneling of the bright one and two soliton is also studied under some Gaussian dispersion or nonlinearity.</p>

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Bright soliton interactions in the variable coefficient Fokas-Lenells equation, Conservation laws, Modulation instability and Soliton tunneling

  • 期刊论文

  • 发表日期：

    2026年3月10日

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  • Sagardeep Talukdar,
  • R. Ramakrishnan,
  • Sudipta Nandy,
  • M. Lakshmanan

摘要

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 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 generalized plane wave against small amplitude perturbation. Thereafter, by using a nonstandard Hirota bilinearization method with the help of 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 suitable choice of dispersion and nonlinearity coefficients. Finally, the dramatic effect of nonlinear tunneling of the bright one and two soliton is also studied under some Gaussian dispersion or nonlinearity.