Totally Nonnegative Pfaffian for Solitons in BKP Equation

TL;DR

This paper introduces a novel approach using totally nonnegative Pfaffians derived from skew Schur Q functions to construct nonsingular line soliton solutions in the BKP equation, revealing complex web-like interactions.

Contribution

It develops a new method to generate nonsingular soliton solutions for the BKP equation using totally nonnegative Pfaffians and explores their interaction patterns.

Findings

Nonsingular line soliton solutions are constructed.

Soliton interactions form web-like structures.

Resonance phenomena are analyzed via Pfaffians.

Abstract

The BKP equation is obtained from the reduction of B type in the KP hierarchy under the orthogonal type transformation group for the KP equation. The skew Schur Q functions can be used to construct the Tau functions of solitons in the BKP equation. Then the totally nonnegative Pfaffian can be defined via the skew Schur Q functions to obtain nonsingular line solitons solution in the BKP equation. The totally nonnegative Pfaffians are investigated. The line solitons interact to form web like structure in the near field region and their resonances appearing in soliton graph could be investigated by the totally nonnegative Pfaffians.