The exact solutions for the non-isospectral Kaup–Newell hierarchy via the inverse scattering transform

Abstract

We begin by introducing a non-isospectral Lax pair, from which we derive a non-isospectral integrable Kaup–Newell hierarchy. The new general solutions for the non-isospectral integrable Kaup–Newell hierarchy are obtained through the inverse scattering transform (IST) method. Finally, we obtain the soliton solutions of a reduced non-isospectral integrable equation from non-isospectral integrable Kaup–Newell hierarchy. For 1-soliton solution, we obtain the explicit expression and analyze the dynamical behavior of soliton solution; for 2-soliton solutions, we verify that collisions between soliton solutions are inelastic collisions. The significant difference of the paper from the works finished by other authors (such as Ning et al., 2004 [11,12]; Li et al., 2008, 2010, 2012) lies in except for the spectral parameter λ being higher order, not one-order of λ.