修正的非线性薛定谔模型、${\cal C}{\cal P}_s{\cal T}_d$对称性、暗孤子和无限大反常电荷塔
Modified non-linear Schrödinger models, ${\cal C}{\cal P}_s{\cal T}_d$ symmetry, dark solitons and infinite towers of anomalous charges
摘要：
一些修正的（散焦的）非线性薛定谔模型（MNLS）拥有无限多的反常守恒律塔和渐近守恒的电荷。对于特殊的${\cal C}{\cal P}_s{\cal T}_d$对称场位形，在时空积分时，所谓的准守恒律反常消失了。通过数值计算与不可积的五阶NLS模型的最低阶准守恒律相关的一些代表性异常，我们数值验证了暗孤子相互作用区域周围电荷的修改程度，作为修改的（散焦）NLS模型。该修改取决于参数$ε$，使得针对$ε=0$恢复标准NLS。本文对小的$|ε|$进行了数值模拟，结果表明两个暗孤子的碰撞是弹性的。NLS型方程在非线性科学的几个领域中相当普遍。
英文摘要：
Some modified (defocusing) non-linear Schrödinger models (MNLS) possess infinite towers of anomalous conservation laws with asymptotically conserved charges. The so-called anomalies of the quasi-conservation laws vanish upon space-time integration for a special ${\cal C}{\cal P}_s{\cal T}_d$ symmetric field configurations. We verify numerically the degree of modifications of the charges around the dark-soliton interaction regions by computing numerically some representative anomalies related to lowest order quasi-conservation laws of the non-integrable cubic-quintic NLS model as a modified (defocusing) NLS model. This modification depends on the parameter $ε$, such that the standard NLS is recovered for $ε=0$. Here we present the numerical simulations for small values of $|ε|$, and show that the collision of two dark solitons are elastic. The NLS-type equations are quite ubiquitous in several areas of non-linear science.
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