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

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Abstract

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.

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Authors and Affiliations

  1. Department of Applied Mathematics, China Agricultural University, Beijing, 100083, China

    XiaoJun Liu & Can Gao

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  1. XiaoJun Liu
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  2. Can Gao
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Correspondence to XiaoJun Liu.

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Liu, X., Gao, C. Generalized dressing method for the extended two-dimensional Toda lattice hierarchy and its reductions. Sci. China Math. 54, 365–380 (2011). https://doi.org/10.1007/s11425-010-4086-4

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