Generalized dressing method for the extended two-dimensional Toda lattice hierarchy and its reductions  

作　　者：LIU XiaoJun GAO Can 

机构地区：[1]Department of Applied Mathematics, China Agricultural University, Beijing 100083, China

出　　处：《Science China Mathematics》2011年第2期365-380,共16页中国科学：数学（英文版）

基　　金：supported by National Basic Research Program of China (973 Program) (Grant No. 2007CB814800);National Natural Science Foundation of China (Grant Nos. 10801083, 10901090);Chinese Universities Scientific Fund (Grant No. 2009-2-05);the Basic Research Fund of China Agricultural University (Grant No. 2007036)

摘　　要：In this paper, we solve the extended two-dimensional Toda lattice hierarchy (ex2DTLH) by the generalized dressing method developed in Liu-Lin-Jin-Zeng (2009). General Casoratian determinant solutions for this hierarchy are obtained. In particular, explicit solutions of soliton-type are formulated by using the τ-function in the form of exponential functions. The periodic reduction and one-dimensional reduction of ex2DTLH are studied by finding the constraints. Many reduced systems are shown, including the periodic ex2DTLH, sinh-Gordon equation with self-consistent sources and one-dimensional Toda lattice hierarchy with self-consistent sources. The general solutions of reduced hierarchies are found from the Casoratian solutions of ex2DTLH, by considering additional constraints during the dressing procedure.In this paper, we solve the extended two-dimensional Toda lattice hierarchy （ex2DTLH） by the generalized dressing method developed in Liu-Lin-Jin-Zeng （2009）. General Casoratian determinant solutions for this hierarchy are obtained. In particular, explicit solutions of soliton-type are formulated by using the τ-function in the form of exponential functions. The periodic reduction and one-dimensional reduction of ex2DTLH are studied by finding the constraints. Many reduced systems are shown, including the periodic ex2DTLH, sinh-Gordon equation with self-consistent sources and one-dimensional Toda lattice hierarchy with self-consistent sources. The general solutions of reduced hierarchies are found from the Casoratian solutions of ex2DTLH, by considering additional constraints during the dressing procedure.

关 键 词：extended Toda lattice hierarchy DRESSING reduction sinh-Gordon self-consistent sources SOLITON 

分 类 号：O4[理学—物理] TP311.13[自动化与计算机技术—计算机软件与理论]