标题： Bäcklund变换，Ward孤子和单位子 显示英文标题

标题： Backlund transformations, Ward solitons, and unitons

摘要： Ward方程，也称为修正的2+1维手征模型，是由自对偶Yang-Mills场方程在$R^{2,2}$上通过维度约化和规范固定得到的。它有一个Lax对，并且是一个可积系统。 Ward构造了扩展解具有不同简单极点的孤立子。 他还使用了一种极限方法来构造扩展解具有二阶极点的2-孤立子。 Ioannidou和Zakrzewski以及Anand构造了更多扩展解具有二阶或三阶极点的孤立子解。 本文的一些主要结果是：(i) 我们构造了代数Bäcklund变换（BT），通过代数方法从给定的一个解生成新的Ward方程解。 (ii) 我们使用一阶$k$极限方法和代数BTs来构造显式的Ward孤立子，其扩展解具有任意极点和重数。 (iii) 我们证明了我们的构造给出了Ward方程的所有孤立子的显式表示，并且Ward孤立子的条目必须是$x, y$和$t$中的有理函数。 (iv) 由于静止的 Ward孤立子是unitons，我们的方法也可以从有限个从$C$到$C^n$的有理映射显式地构造所有$k$-unitons。 显示英文摘要

摘要： The Ward equation, also called the modified 2+1 chiral model, is obtained by a dimension reduction and a gauge fixing from the self-dual Yang-Mills field equation on $R^{2,2}$. It has a Lax pair and is an integrable system. Ward constructed solitons whose extended solutions have distinct simple poles. He also used a limiting method to construct 2-solitons whose extended solutions have a double pole. Ioannidou and Zakrzewski, and Anand constructed more soliton solutions whose extended solutions have a double or triple pole. Some of the main results of this paper are: (i) We construct algebraic B\"acklund transformations (BTs) that generate new solutions of the Ward equation from a given one by an algebraic method. (ii) We use an order $k$ limiting method and algebraic BTs to construct explicit Ward solitons, whose extended solutions have arbitrary poles and multiplicities. (iii) We prove that our construction gives all solitons of the Ward equation explicitly and the entries of Ward solitons must be rational functions in $x, y$ and $t$. (iv) Since stationary Ward solitons are unitons, our method also gives an explicit construction of all $k$-unitons from finitely many rational maps from $C$ to $C^n$.