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Variable-coefficient nonisospectral Toda lattice hierarchy; exact solution; compatibility condition; inverse scattering transformation.

In this paper, a hierarchy of nonisospectral equations with variable coefficients is derived from the compatibility condition of Toda spectral problem and its time evolution. In order to solve the derived Toda lattice hierarchy, the inverse scattering transformation is utilized. As a result, new and more general exact solutions are obtained. It is shown that the inverse scattering transformation can be generalized to solve some other nonisospectral lattice hierarchies with variable coefficients.

Sheng Zhang¹ Di Wang¹

1. School of Mathematics and Physics, Bohai University, Jinzhou 121013, People's Republic of China

Manuscript received

14 May 2014

Manuscript revised

6 August 2014

Accepted

21 August 2014

Early published

3 May 2015