Dualism in the Theory of Soliton Solutions II

This paper is a continuation of the work by L.A. Belkaryan and A.L. Belkaryan published in this journal (64 (7), 1472–1490 (2024)). A theorem is proved formulated as a conjecture in the preceding paper stating the existence and uniqueness of soliton solutions and corresponding solutions of the functional differential equation from a dual pair “function–operator.” For the model of traffic flow on a Manhattan lattice, this result is used to study soliton solutions with more complicated characteristics than those specified by an additive cyclic subgroup of $$\mathbb{R}$$ .