ABSTRACT

In this paper, we derive the solitons solutions to the cubic–quartic nonlinear Schrödinger equation (CQ-NLSE) in birefringent fibers with three laws of nonlinearity. These laws are parabolic law, quadratic-cubic law and non-local law. The new extended generalized Kudryashov method and our new method proposed for the first time have been applied. Many solutions have been found. Dark, bright and singular soliton solutions existed under constraint conditions. The comparative analysis of the two proposed methods shows that in the two cases of parabolic and non-local laws, the first method gives the dark and singular solitons in terms of tanh–coth hyperbolic functions, respectively, while the second method gives the bright and singular solitons in terms of sech–csch hyperbolic functions, respectively. But in the case of quadratic-cubic law, both methods give the bright-singular solitons in terms of sech${}^2$–csch${}^2$ hyperbolic functions, respectively, with different arguments.

摘要

在本文中，我们推导了具有三个非线性定律的双折射光纤中三次-四次非线性薛定谔方程 (CQ-NLSE) 的孤子解。这些定律是抛物线定律、二次三次定律和非局部定律。新的扩展广义 Kudryashov 方法和我们首次提出的新方法已得到应用。已经找到了许多解决方案。在约束条件下存在暗、亮和奇异孤子解。对所提出的两种方法的比较分析表明，在抛物线和非局部定律的两种情况下，第一种方法以tanh - coth的形式给出了暗孤子和奇异孤子。双曲函数，而第二种方法分别根据 sech-csch 双曲函数给出亮孤子和奇异孤子。但是在二次三次定律的情况下，两种方法都给出了明亮奇异孤子的 sech${}^2$-csch${}^2$双曲函数，分别具有不同的参数。