五阶非线性作用下光纤中类明孤子运动方程的变分研究

当考虑到五阶非线性对光脉冲传输的影响时, 光纤中类明孤子的传输服从含五阶非线性修正项的非线性Schrdinger方程。利用何氏半反推法建立该类明孤子运动方程的变分形式, 然后应用何氏变分法导出该方程基态孤子解的双曲正割表达式。同时, 受何氏指数函数方法的启发, 建立了一种新的高斯表达式。一方面, 基于得到的显式表达式相关学者可进一步研究五阶非线性对光脉冲传输的影响。另一方面, 该求解过程也进一步显示了用何氏变分法求解数学物理中非线性发展方程的简洁有效性。

A Variational Study on the Propagation Equation of Bright Soliton-Like Pulse Under the Influence of the Fifth-Order Nonlinearity in Optical Fiber

When considering the influence of the fifth-order nonlinearity on the propagation of optical pulse, the propagation of bright soliton-like pulse in optical fiber satisfies the following nonlinear Schrdinger equation with the fifth-order nonlinear term. By using of He′s semi-inverse method, the variational form to this equation is established firstly. Then, the Sech expression formula to the traveling wave solution of the equation is derived by utilizing He′s variational method. At the same time, motivatied by He′s exp-function method, a new Guass expression formula of the solution is obtained. On the one hand, one can further study the influence of fifth-order nonlinearity on the propagation of pulse in optical fiber based on these expression formulae. On the other hand, the solution process reveals that He′s variational method is an easy, concise and effective method to solve nonlinear evolution equations arising in mathematical physics.