This is the 1st publication to regard combinatorial and geometric features of two-dimensional solitons. in response to fresh examine by means of the writer and his collaborators, the publication offers new advancements keen on an interaction among the idea of solitons and the combinatorics of finite-dimensional Grassmannians, specifically, the definitely nonnegative (TNN) components of the Grassmannians.

The booklet starts with a short creation to the idea of the Kadomtsev–Petviashvili (KP) equation and its soliton recommendations, referred to as the KP solitons. as a result of the nonlinearity within the KP equation, the KP solitons shape very advanced yet attention-grabbing web-like styles in dimensions. those styles are known as soliton graphs. The major objective of the e-book is to enquire the designated constitution of the soliton graphs and to categorise those graphs. It seems that the matter has an intimate reference to the research of the TNN a part of the Grassmannians. The publication additionally offers an easy creation to the hot improvement of the combinatorial point of the TNN Grassmannians and their parameterizations, so that it will be worthwhile for fixing the type problem.

This paintings appeals to readers attracted to actual algebraic geometry, combinatorics, and soliton thought of integrable platforms. it could function a useful reference for knowledgeable, a textbook for a distinct themes graduate direction, or a resource for self sustaining examine tasks for complicated upper-level undergraduates focusing on physics and mathematics.