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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.