2017/11/25 by Zhenya Yan, Yan, Zhenya
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Combinatorics #Conservation law #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Geometry #Hierarchy #Integrable system #Law #Mathematical Physics (math-ph) #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum mechanics #Schrödinger equation #Symmetry (geometry) #math-ph #math.AP #math.MP #nlin.SI #quant-ph
paper · pdf · doi:10.48550/arxiv.1711.09222
published in arXiv (Cornell University) (Cornell University) · 8 pages
arxiv created 2017/11/25 · openalex publication_date 2017/11/25 · arxiv updated 2017/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We use two families of parameters \(εxj, εtj) | εxj,tj=±1, j=1,2,...,n\ to first introduce a unified novel two-family-parameter system (simply called \mathcal Q(n)_ε_x_n,ε_t_n system), connecting integrable local, nonlocal, novel mixed-local-nonlocal, and other nonlocal vector nonlinear Schrödinger (VNLS) equations. The \mathcal Q(n)_ε_x_n, ε_t_n system with (εxj, εtj)=(± 1, 1), j=1,2,...,n is shown to possess Lax pairs and infinite number of conservation laws. Moreover, we also analyze the \mathcal PT symmetry of the Hamiltonians with self-induced potentials. The multi-linear forms and some symmetry reductions are also studied. In fact, the used two families of parameters can also be extended to the general case \(εxj, εtj) | εxj = e^iθxj, εtj = e^iθtj, θxj, θtj∈ [0, 2π), j=1,2,...,n\ to generate more types of nonlinear equations. The two-family-parameter idea used in this paper can also be applied to other local nonlinear evolution equations such that novel integrable and non-integrable nonlocal and mixed-local-nonlocal systems can also be found.