Backlund transformations, ward solitons,and unitons

Bo Dai Peking University Chuu-Lian Terng Northeastern University

Differential Geometry mathscidoc:1609.10002

Journal of Differential Geometry, 75, 57-108, 2007
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 R2,2. It has a Lax pair and is an integrable system. Ward constructed solitons whose ex- tended 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 finite sequences of rational maps from C to Cn.
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  author={Bo Dai, and Chuu-Lian Terng},
  booktitle={Journal of Differential Geometry},
Bo Dai, and Chuu-Lian Terng. BACKLUND TRANSFORMATIONS, WARD SOLITONS,AND UNITONS. 2007. Vol. 75. In Journal of Differential Geometry. pp.57-108.
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