Pfaffian form of the Grammian determinant solutions of the BKP hierarchy
Q. P. Liu, Manuel Manas
TL;DR
This paper demonstrates how Grammian determinant solutions of the KP hierarchy can be reduced to Pfaffian solutions of the BKP hierarchy using specific differential constraints on transformation data.
Contribution
It introduces a method to derive Pfaffian solutions of the BKP hierarchy from Grammian determinants of the KP hierarchy via differential constraints.
Findings
Reduction from Grammian to Pfaffian solutions achieved
Explicit Pfaffian solutions constructed for the BKP hierarchy
Method enhances understanding of solution structures in integrable systems
Abstract
The Grammian determinant type solutions of the KP hierarchy, obtained through the vectorial binary Darboux transformation, are reduced, imposing suitable differential constraint on the transformation data, to Pfaffian solutions of the BKP hierarchy.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Topics in Algebra · Advanced Differential Equations and Dynamical Systems