N-soliton-like and double Casoratian solutions of a nonisospectral Ablowitz–Ladik equation

Abstract

A bilinear form of a nonisospectral differential-difference equation related to the Ablowitz–Ladik (AL) spectral problem is derived by a transformation of dependent variables. Exact solutions to the resulting bilinear equation are found. The [Formula: see text]-soliton-like solutions and the double Casoratian solutions are derived by means of Hirota’s direct method and the double Casoratian technique, respectively. Moreover, the connection between those two classes of solutions is explored.

Soliton Solutions for a Nonisospectral Semi-Discrete Ablowitz–Kaup–Newell–Segur Equation

“…In [27,28], Inverse Scattering Transform was used to construct multisoliton solutions of the nonisospectral Ablowitz-Ladik hierarchy. Recently, N-soliton solutions to a nonisospectral Ablowitz-Ladik type equation have been investigated by using the Hirota's method and Casorati technique [29]. In addition, based on Hankel type determinants, Chen et al present solutions for a nonisospectral Toda lattice [30] as well as the first and second members in the nonisospectral extended Volterra lattice hierarchy [31].…”