论文标题
修改的非线性schrödinger模型，$ {\ cal c} {\ cal p} _s {\ cal t} _d $不变$ n- $ n- $ bright solitons and Infinite tower
Modified non-linear Schrödinger models, ${\cal C}{\cal P}_s{\cal T}_d$ invariant $N-$bright solitons and infinite towers of anomalous charges
论文作者
论文摘要
非线性schrödinger模型（MNLS）$ i \ partial_ {t}ψ（x，x，t） + \ partial^2_ {x}ψ（x，x，t） - [\ frac {ΔV} {Δv} {δ|^2}] @ = 0， \ rightarrow r $被考虑。我们表明，MNLS模型具有无限保存法律的无限塔，用于具有特殊复杂的共轭，改变平价和延迟的时间归还（$ {\ cal c} {\ cal p} {\ cal p} _s _s {\ cal t} _d $）对称性。即使在标准的NLS模型中出现了异常电荷的无限塔，$ {\ cal c} {\ cal p} _s {\ cal t} _d _d $不变$ n- $ n- $ bright solitons。真正的保守电荷通过某种异常取消机制出现。引入了针对修改后的AKNS系统（MAKNS）引入双重RICCATI-Type伪电势配方，并发现了新型异常保护定律的无限塔。此外，在线性系统公式中发现了精确非本地保护定律的无限塔。我们的分析结果得到了$ 2- $ bright-Soliton散射的数值模拟，具有$ v = - \ frac {2η} {2+ε}（|ψ|^|^2）^{2 +ε}，ε}，ε\ in r，η> 0 $。我们的数值模拟显示了亮孤子的弹性散射，用于集合$ \ {η，ε\} $的广泛值以及各种振幅和相对速度。 AKNS-type系统无处不在，因此，我们的结果可能在非线性物理学的几个领域中发现了潜在的应用，例如Bose-Einstein凝结，超导性，独感湍流以及仪表理论中的试验性，综合模型和重力理论。
Modifications of the non-linear Schrödinger model (MNLS) $ i \partial_{t} ψ(x,t) + \partial^2_{x} ψ(x,t) - [\frac{δV}{δ|ψ|^2} ] ψ(x,t) = 0,$ where $ψ\in C$ and $V: R_{+} \rightarrow R$, 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 (${\cal C}{\cal P}_s{\cal T}_d$) symmetry. Infinite towers of anomalous charges appear even in the standard NLS model for ${\cal C}{\cal P}_s{\cal T}_d$ invariant $N-$bright solitons. The true conserved charges emerge through some kind of anomaly cancellation mechanism. A dual Riccati-type pseudo-potential formulation is introduced for a modified AKNS system (MAKNS) and infinite towers of novel anomalous conservation laws are uncovered. In addition, infinite towers of exact non-local conservation laws are uncovered in a linear system formulation. Our analytical results are supported by numerical simulations of $2-$bright-soliton scatterings with potential $ V = - \frac{ 2η}{2+ ε} ( |ψ|^2 )^{2 + ε}, ε\in R, 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 AKNS-type system is quite ubiquitous, and so, our results may find potential applications in several areas of non-linear physics, such as Bose-Einstein condensation, superconductivity, soliton turbulence and the triality among gauge theories, integrable models and gravity theories.
