Real Line Solitons of the BKP Equation

TL;DR

This paper explores the structure of real line solitons in the BKP equation using Pfaffian and Grassmannian methods, deriving explicit N-soliton solutions and their Tau functions.

Contribution

It introduces a novel approach to analyze real line solitons of the BKP equation via totally non-negative Grassmannian and constructs explicit N-soliton solutions.

Findings

Explicit N-soliton solutions for the BKP equation are obtained.

The self-dual Tau function for these solutions is derived.

The Grassmannian framework is extended to the Sawada-Kotera equation.

Abstract

The solitons solution of BKP equation can be constructed by the Pfaffian structure. Then one investigates the real line solitons structure of BKP equation using the totally non-negative Grassmannian. Especially, the N-soliton solution is studied and its self-dual Tau function is obtained. Also, one can construct the totally non-negative Grassmannian of the Sawada-Kotera equation for its real line solitons.