A note on reductions of the dispersionless Toda hierarchy

Abstract

We investigate the algebraic structure of the dispersionless Hirota equations for the m + 1-variable reductions of the dispersionless Toda hierarchy which contains the special case for m = 1 considered by Kodama and Pierce. We demonstrate the m = 2 case to illustrate the obtained result. C

A Toda lattice hierarchy with variable coefficients and its multi-wave solutions

“…Constructing such types of NLEE and obtaining their exact solutions often play an important role in helping us understand these phenomena. Since Ablowitz successfully solved the isospectral Toda equation, there has been various works for the Toda hierarchy, such as those in [2][3][4], but almost of these works focus on constant-coefficient hierarchy. In this paper, starting from the Toda spectral problem, we shall construct a new Toda lattice hierarchy with variable coefficients and then construct its multi-wave solutions.…”