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 $\tan$ function and the Schur identity. By the minor-summation formula of the Pfaffian, we can study the interactions of solitons in the Novikov-Veselov equation from the Kadomtsev-Petviashvili (KP) equation's point of view, that is, the totally non-negative Grassmannian. Especially, the Y-shape 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 are computed and one makes a comparison with the KP-(II) equation.

24 pages, 3 figures

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Cited by in corpus (3)

• Mach-Type Soliton in the Novikov-Veselov Equation
• Soliton Interaction In the Modified Kadomtsev-Petviashvili-(II) Equation
• The resonant structure of Kink-Solitons in the Modified KP Equation