Modified AKNS model, Riccati-type pseudo-potential approach and infinite towers of quasi-conservation laws

Modified non-linear Schrödinger models, ${\cal C}{\cal P}_s{\cal T}_d$ invariant $N-$bright solitons and infinite towers of anomalous charges

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 charg…

Riccati-type pseudopotentials, conservation laws and solitons of deformed sine-Gordon models

Deformed sine-Gordon (DSG) models $\partial_ξ\partial_η\, w + \frac{d}{dw}V(w) = 0$, with $V(w)$ being the deformed potential, are considered in the context of the Riccati-type pseudopotential approach. A compatibility condition of the deformed system of Riccati-type equations reproduces the equation of motion of the DSG models. Then, we provide a pair of linear systems of equations for DSG model, and provide an infinite tower of non-local conservation laws. Through a direct construction and supported by numerical simulations of soliton scatterings, we show that the DSG models, which have rece…

Riccati型伪势方法在变形孤子理论准可积性中的应用

Riccati-type pseudo-potential approach to quasi-integrability of deformed soliton theories

本文综述了Riccati型伪势方法在准可积sine-Gordon、KdV和NLS模型中的应用，提出统一框架分析多种变形可积系统，发现异常守恒定律和非局域守恒定律，对非线性物理多个领域具有潜在应用价值。

Quasi-integrable KdV models, towers of infinite number of anomalous charges and soliton collisions

We found, through analytical and numerical methods, new towers of infinite number of asymptotically conserved charges for deformations of the Korteweg-de Vries equation (KdV). It is shown analytically that the standard KdV also exhibits some towers of infinite number of anomalous charges, and that their relevant anomalies vanish for $N-$soliton solution. Some deformations of the KdV model are performed through the Riccati-type pseudo-potential approach, and infinite number of exact non-local conservation laws is provided using a linear formulation of the deformed model. In order to check the d…