Linear integral equations, infinite matrices, and soliton hierarchies

Wei Fu; Frank W. Nijhoff

doi:10.1063/1.5046684

Linear integral equations, infinite matrices, and soliton hierarchies

Wei Fu^*
, Frank W. Nijhoff

^*Corresponding author for this work

University of Leeds

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

A systematic framework is presented for the construction of hierarchies of soliton equations. This is realised by considering scalar linear integral equations and their representations in terms of infinite matrices, which give rise to all (2 + 1)- and (1 + 1)-dimensional soliton hierarchies associated with scalar differential spectral problems. The integrability characteristics for the obtained soliton hierarchies, including Miura-type transforms, τ-functions, Lax pairs, and soliton solutions, are also derived within this framework.

Original language	English
Article number	071101
Journal	Journal of Mathematical Physics
Volume	59
Issue number	7
DOIs	https://doi.org/10.1063/1.5046684
State	Published - 1 Jul 2018
Externally published	Yes

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title = "Linear integral equations, infinite matrices, and soliton hierarchies",

abstract = "A systematic framework is presented for the construction of hierarchies of soliton equations. This is realised by considering scalar linear integral equations and their representations in terms of infinite matrices, which give rise to all (2 + 1)- and (1 + 1)-dimensional soliton hierarchies associated with scalar differential spectral problems. The integrability characteristics for the obtained soliton hierarchies, including Miura-type transforms, τ-functions, Lax pairs, and soliton solutions, are also derived within this framework.",

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AB - A systematic framework is presented for the construction of hierarchies of soliton equations. This is realised by considering scalar linear integral equations and their representations in terms of infinite matrices, which give rise to all (2 + 1)- and (1 + 1)-dimensional soliton hierarchies associated with scalar differential spectral problems. The integrability characteristics for the obtained soliton hierarchies, including Miura-type transforms, τ-functions, Lax pairs, and soliton solutions, are also derived within this framework.

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Linear integral equations, infinite matrices, and soliton hierarchies

Abstract

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