Soliton generation and conservation laws for vector light pulses propagating in weakly birefringent waveguides

IF 2.1 3区 物理与天体物理 Q2 ACOUSTICS Wave Motion Pub Date : 2024-06-08 DOI:10.1016/j.wavemoti.2024.103356
J.C. Ndogmo , H.Y. Donkeng
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Abstract

The principal algebra Lp of coupled nonlinear Schrödinger equations describing the propagation of polarized optical pulses and involving four-wave mixing terms is obtained in terms of the three arbitrary labelling parameters of the system of equations. This algebra is found to be five-dimensional, indicating the richness in symmetries of the system. The most general symmetry group transformation by generators of Lp is found and it is shown that this transformation preserves the boundedness of solutions, and an example of transformation of a soliton solution into a completely new soliton of a different type is presented. Moreover, it is explained how an infinite sequence of bounded solutions can thus be generated, yielding new solitons. Several other important properties of solutions and symmetry group transformations of the system are also demonstrated. As the system of Schrödinger equations under study turns out to be of Lagrange type, conservation laws associated with all variational symmetries of Lp are constructed and interpreted. Some symmetry reductions of the system are also derived.

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在弱双折射波导中传播的矢量光脉冲的孤子产生和守恒定律
描述偏振光脉冲传播并涉及四波混合项的耦合非线性薛定谔方程的主代数 Lp 是根据方程系统的三个任意标注参数得到的。发现该代数是五维的,表明该系统具有丰富的对称性。通过 Lp 的生成器找到了最一般的对称群变换,并证明这种变换保留了解的有界性,还给出了一个将孤子解变换为不同类型的全新孤子的例子。此外,还解释了有界解的无限序列是如何产生的,从而产生新的孤子。此外,还展示了解的其他一些重要特性以及系统的对称群变换。由于所研究的薛定谔方程组属于拉格朗日类型,因此构建并解释了与 Lp 所有变分对称性相关的守恒定律。此外,还推导出了该系统的一些对称性还原。
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来源期刊
Wave Motion
Wave Motion 物理-力学
CiteScore
4.10
自引率
8.30%
发文量
118
审稿时长
3 months
期刊介绍: Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics. The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.
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