Explicit solution and Darboux transformation for a new discrete integrable soliton hierarchy with 4×4 Lax pairs | Zendy

yu Fajun | Zendy; Feng Shuo | Zendy

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Explicit solution and Darboux transformation for a new discrete integrable soliton hierarchy with 4×4 Lax pairs

Author(s) -

yu Fajun,

Feng Shuo

Publication year - 2017

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.4406

Subject(s) - integrable system , mathematics , lax pair , hierarchy , transformation (genetics) , lattice (music) , soliton , darboux integral , toda lattice , pure mathematics , mathematical analysis , algebra over a field , quantum mechanics , nonlinear system , physics , law , geometry , biochemistry , chemistry , curvature , gene , political science , acoustics

The Darboux transformation method with 4×4 spectral problem has more complexity than 2×2 and 3×3 spectral problems. In this paper, we start from a new discrete spectral problem with a 4×4 Lax pairs and construct a lattice hierarchy by properly choosing an auxiliary spectral problem, which can be reduced to a new discrete soliton hierarchy. For the obtained lattice integrable coupling equation, we establish a Darboux transformation and apply the gauge transformation to a specific equation and then the explicit solutions of the lattice integrable coupling equation are obtained. Copyright © 2017 John Wiley & Sons, Ltd.

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