N-fold Darboux transformation and soliton solutions for the relativistic
Toda lattice equation
Abstract
In this paper, the relativistic Toda lattice (RTL) equation is
investigated via N-fold Darboux transformation (DT) technique. Basing on
the Lax pair and gauge transformation, we construct N-fold DT of the RTL
equation, and derive two kinds of the N-fold explicit exact solutions
from two different seed solutions. Structures of the one-, two-, three-
and four-soliton solutions and periodic solutions which have important
applications are shown graphically. By studying the elastic interactions
among four-soliton solutions, we confirm those solutions’ shapes and
amplitudes don’t change after the interaction, which are the main
characteristics of solitons. In particular, we present the relationship
between the structures of exact solutions and the parameters with N=1.
Results in this paper might be helpful for interpreting certain physical
phenomena.