关于非手性中间长波方程II：周期情形

关于非手性中间长波方程

On the non-chiral intermediate long wave equation

本文研究非手性中间长波方程的可积性，通过推导Lax对、Hirota双线性形式、Bäcklund变换及无穷多守恒律，证明其可积性。

Non-chiral Intermediate Long Wave equation and inter-edge effects in narrow quantum Hall systems

We present a non-chiral version of the Intermediate Long Wave (ILW) equation that can model nonlinear waves propagating on two opposite edges of a quantum Hall system, taking into account inter-edge interactions. We obtain exact soliton solutions governed by the hyperbolic Calogero-Moser-Sutherland (CMS) model, and we give a Lax pair, a Hirota form, and conservation laws for this new equation. We also present a periodic non-chiral ILW equation, together with its soliton solutions governed by the elliptic CMS model.

非手征中间海森堡铁磁体方程的周期解，由椭圆自旋Calogero-Moser动力学描述

Periodic solutions of the non-chiral intermediate Heisenberg ferromagnet equation described by elliptic spin Calogero-Moser dynamics

本文构造了非手征中间海森堡铁磁体方程的周期解，利用椭圆自旋Calogero-Moser系统及其新Bäcklund变换实现。

Periodic and homoclinic solutions of the modified 2+1 Chiral model

We use algebraic Backlund transformations (BTs) to construct explicit solutions of the modified 2+1 chiral model from $T^2\times R$ to SU(n), where $T^2$ is a 2-torus. Algebraic BTs are parameterized by $z\in C$ (poles) and holomorphic maps $π$ from $T^2$ to Gr$(k,C^n)$. We apply Bäcklund transformations with carefully chosen poles and $π$'s to construct infinitely many solutions of the 2+1 chiral model that are (i) doubly periodic in space variables and periodic in time, i.e., triply periodic, (ii) homoclinic in the sense that the solution $u$ has the same stationary limit $u_0$ as $t\to \pm\…

自旋非手性中间长波方程的椭圆孤子解

Elliptic soliton solutions of the spin non-chiral intermediate long-wave equation

本文通过自旋极点拟设和含动力学背景项的椭圆 A 型自旋 Calogero-Moser 系统，构造了周期边界条件下自旋非手性中间长波方程的椭圆多孤子解，并推广到实直线及自旋 Benjamin-Ono 方程。

The non-chiral intermediate Heisenberg ferromagnet equation

We present and solve a soliton equation which we call the non-chiral intermediate Heisenberg ferromagnet (ncIHF) equation. This equation, which depends on a parameter $δ>0$, describes the time evolution of two coupled spin densities propagating on the real line, and in the limit $δ\to \infty$ it reduces to two decoupled half-wave maps (HWM) equations of opposite chirality. We show that the ncIHF equation is related to the A-type hyperbolic spin Calogero-Moser (CM) system in two distinct ways: (i) it is obtained as a particular continuum limit of a Inozemtsev-type spin chain related to this CM …