تقرير
Modified non-linear Schr\'odinger models, ${\cal C}{\cal P}_s{\cal T}_d$ invariant $N-$bright solitons and infinite towers of anomalous charges
| العنوان: | Modified non-linear Schr\'odinger models, ${\cal C}{\cal P}_s{\cal T}_d$ invariant $N-$bright solitons and infinite towers of anomalous charges |
|---|---|
| المؤلفون: | Blas, H., Maguiña, M. Cerna, Santos, L. F. dos |
| سنة النشر: | 2020 |
| المجموعة: | Mathematics High Energy Physics - Theory Mathematical Physics Nonlinear Sciences |
| مصطلحات موضوعية: | High Energy Physics - Theory, Mathematical Physics, Nonlinear Sciences - Pattern Formation and Solitons, Nonlinear Sciences - Exactly Solvable and Integrable Systems |
| الوصف: | Modifications of the non-linear Schr\"odinger model (MNLS) $ i \partial_{t} \psi(x,t) + \partial^2_{x} \psi(x,t) - [\frac{\delta V}{\delta |\psi|^2} ] \psi(x,t) = 0,$ where $\psi \in C$ 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{ 2\eta}{2+ \epsilon} ( |\psi|^2 )^{2 + \epsilon}, \epsilon \in R, \eta>0$. Our numerical simulations show the elastic scattering of bright solitons for a wide range of values of the set $\{\eta, \epsilon\}$ 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. Comment: 58 pages, 15 figures. A new section added with derivations of novel anomalous charges in the pseudo-potential approach. A recent Ref. (arXiv:2102.07190 [hep-th]) about similar results on dark-soliton simulations has been added |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1142/S0217979221502726 |
| URL الوصول: | http://arxiv.org/abs/2007.13910 |
| رقم الأكسشن: | edsarx.2007.13910 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1142/S0217979221502726 |
|---|