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Modified nonlinear Schrödinger models, 𝒞𝒫s𝒯d invariant N-bright solitons and infinite towers of anomalous charges
International Journal of Modern Physics B ( IF 1.7 ) Pub Date : 2021-09-10 , DOI: 10.1142/s0217979221502726
H. Blas 1 , M. Cerna Maguiña 2 , L. F. dos Santos 3
Affiliation  

Modifications of the nonlinear Schrödinger (MNLS) model itψ(x,t) + x2ψ(x,t) [ δV δ|ψ|2 ]ψ(x,t) = 0, where ψ and V : IR+ IR, are considered. We show that the MNLS models possess infinite towers of quasi-conservation laws for soliton-type configurations with a special complex conjugation, shifted parity and delayed time reversion (𝒞𝒫s𝒯d) symmetry. Infinite towers of anomalous charges appear even in the standard NLS model for 𝒞𝒫s𝒯d invariant N-bright solitons. The true conserved charges emerge through some kind of anomaly cancellation mechanism. Our analytical results are supported by numerical simulations of two-bright-soliton scatterings with potential V = 2η 2+𝜖(|ψ|2)2+𝜖,𝜖 IR,η > 0. Our numerical simulations show the elastic scattering of bright solitons for a wide range of values of the set {η,𝜖} and a variety of amplitudes and relative velocities. The MNLS-type systems are quite ubiquitous, and so, our results may find potential applications in several areas of nonlinear physics, such as Bose–Einstein condensation, superconductivity, soliton turbulence and the triality among gauge theories, integrable models and gravity theories.

中文翻译:

修正的非线性薛定谔模型,𝒞𝒫s𝒯d 不变的 N 亮孤子和无限的异常电荷塔

非线性薛定谔 (MNLS) 模型的修改一世ψ(X,) + X2ψ(X,) - [ δ δ|ψ|2 ]ψ(X,) = 0,在哪里ψ 红外+ 红外, 被考虑。我们证明了 MNLS 模型对于具有特殊复共轭、移位奇偶校验和延迟时间反转的孤子型构型具有无限的准守恒定律塔(𝒞𝒫s𝒯d) 对称性。即使在标准 NLS 模型中也出现了无限的异常电荷塔𝒞𝒫s𝒯d不变的ñ-明亮的孤子。真正的守恒电荷是通过某种异常消除机制出现的。我们的分析结果得到了具有势能的两个亮孤子散射的数值模拟的支持 = - 2η 2+𝜖(|ψ|2)2+𝜖,𝜖 红外,η > 0. 我们的数值模拟显示了明亮孤子的弹性散射对于广泛的集合值{η,𝜖}以及各种幅度和相对速度。MNLS型系统非常普遍,因此,我们的研究结果可能会在非线性物理的多个领域中找到潜在的应用,例如玻色-爱因斯坦凝聚、超导、孤子湍流以及规范理论、可积模型和引力理论之间的试验。
更新日期:2021-09-10
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