Special soliton solutions to the Toda lattice hierarchy (Q2455333)

The author deals with the system of equations \[ \begin{aligned} \varepsilon {\partial u\over\partial t}&= \frac12[(u(x+ \varepsilon)+ u(x)] e^{v(x+\varepsilon)}- (u(x- \varepsilon)+ u(x)) e^{v(x)}],\\ \varepsilon{\partial v\over\partial t}&= \frac12 [e^{v(x+\varepsilon)}- e^{v(x-\varepsilon)}+ u^2(x)- u^2(x- \varepsilon)]\end{aligned}\tag{1} \] and studies two-soliton solutions to system (1) that describe pairwise interactions of solutions. The author shows the existence of several types of solutions that can turn into each other when interacting. Examples of such interactions are given.