On the N-Solitons Solutions in the Novikov-Veselov Equation

Abstract

We construct the $N$-solitons solution in the Novikov-Veselov equation from the extended Moutard transformation and the Pfaffian structure. Also, the corresponding wave functions are obtained explicitly. As a result, the property characterizing the $N$-solitons wave function is proved using the Pfaffian expansion. This property corresponding to the discrete scattering data for $N$-solitons solution is obtained in [arXiv:0912.2155] from the $\bar{\partial }$-dressing method.

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Cited by in corpus (3)

• Mach-Type Soliton in the Novikov-Veselov Equation
• The Interactions of Solitons in the Novikov-Veselov Equation
• The Cauchy problem for the generalized hyperbolic Novikov-Veselov equation via the Moutard symmetries