We investigate non-autonomous solitons in a general coherently coupled nonlinear Schrödinger (CCNLS) system with temporally modulated nonlinearities and with an external harmonic oscillator potential. This general CCNLS system encompasses three distinct types of CCNLS equations that describe the dynamics of beam propagation in an inhomogeneous Kerr-like nonlinear optical medium for different choices of nonlinear polarizations owing to the anisotropy of the medium. We identify a generalized similarity transformation to relate the considered model into the standard integrable homogeneous coupled nonlinear evolution equations with constant nonlinearities, accompanied by a constraint relation expressed in the form of the Riccati equation. With the help of a non-standard Hirota’s bilinearization method and exact soliton solutions, we explore the impact of varying nonlinearities and refractive index in the propagation and collisions analytically by reverse engineering. Interestingly, ...

中文翻译：

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具有可变非线性的非均匀相干耦合非线性Schrödinger模型系统中的矢量孤子的操纵

我们研究具有时间调制非线性和外部谐波振荡器电势的通用相干耦合非线性Schrödinger（CCNLS）系统中的非自治孤子。这个通用的CCNLS系统包含三种不同类型的CCNLS方程，这些方程描述了由于介质各向异性而对非线性偏振的不同选择，从而在不均匀的Kerr类非线性光学介质中传播光束的动力学。我们确定了广义相似度变换，以将考虑的模型关联到具有恒定非线性的标准可积分齐次耦合非线性演化方程，并伴随以Riccati方程形式表示的约束关系。借助非标准Hirota的双线性化方法和精确的孤子解，我们通过逆向工程分析地分析了变化的非线性和折射率对传播和碰撞的影响。有趣的是...