The interactions of solitons in the Novikov–Veselov equation

Abstract

Using the reality condition of the solutions, one constructs the real Pfaffian N-solitons solutions of the Novikov–Veselov (NV) equation using the function and the Schur identity. By the minor-summation formula of the Pfaffian, we can study the interactions of solitons in the NV equation from the Kadomtsev–Petviashvili (KP) equation’s point of view, that is, the totally non-negative Grassmannian. Especially, the Y-type resonance, O-type, and the P-type interactions of X-shape are investigated. Also, the maximum amplitude of the intersection of the line solitons and the critical angle is computed. In addition, one makes a comparison with the KP-(II) equation.

Keywords:

• Pfaffian
• Grassmannian
• real N-solitons
• interactions
• maximum amplitude

AMS Subject Classifications:

• 15A15
• 15A24
• 35A22
• 35C08

Acknowledgements

The author is grateful to Prof. Y. Kodama for valuable discussions. He also thanks Prof. K. Maruno for his suggestions.

Notes

No potential conflict of interest was reported by the author.

Additional information

Funding

This work is supported in part by the National Science Council of Taiwan [grant number NSC 101-2115-M-606-001].