A generalized integrable lattice hierarchy related to the Ablowitz–Ladik lattice: Conservation law, Darboux transformation and exact solution
Fangcheng Fan,
Weikang Xie
Abstract:Under investigation in this paper is a more general discrete [Formula: see text] matrix spectral problem. Starting from this spectral problem, the positive and negative integrable lattice hierarchies are constructed based on the Tu scheme, then by considering linear combination of the positive and negative lattice hierarchies, we give a more general integrable lattice hierarchy, which can reduce to the well-known Ablowitz–Ladik lattice and the discrete modified Korteweg–de Vries (mKdV) equation. In particular,… Show more
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