Moubissi A B, Nakkeeran K, Abobaker Abdosllam M
Département de Physique de l'Université des Sciences et Techniques de Masuku, B.P. 943 Franceville, Gabon.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Aug;76(2 Pt 2):026603. doi: 10.1103/PhysRevE.76.026603. Epub 2007 Aug 8.
By means of the variational formalism for the nonlinear Schrödinger equation, we find an explicit relation for the power of a pulse in terms of its duration, chirp and fiber parameters (group-velocity dispersion and self-phase modulation parameters). Then, using that relation, we derive the explicit analytical expressions for the variational equations corresponding to the amplitude, width, and chirp of the pulse. The derivation of the analytical expressions for the variational equations is possible for the condition when the Hamiltonian of the system is zero. Finally, for Gaussian and hyperbolic secant ansatz, we show good agreement between the results obtained from the analytical expressions and the direct numerical simulation of the nonlinear Schrödinger equation.
通过非线性薛定谔方程的变分形式，我们得到了脉冲功率与其持续时间、啁啾和光纤参数（群速度色散和自相位调制参数）之间的明确关系。然后，利用该关系，我们推导出了与脉冲幅度、宽度和啁啾相对应的变分方程的显式解析表达式。当系统哈密顿量为零时，才有可能推导变分方程的解析表达式。最后，对于高斯和双曲正割假设，我们表明从解析表达式得到的结果与非线性薛定谔方程的直接数值模拟结果吻合良好。
