A large time asymptotics for transparent potentials for the Novikov-Veselov equation at positive energy

Abstract

In the present paper we begin studies on the large time asymptotic behavior for solutions of the Cauchy problem for the Novikov--Veselov equation (an analog of KdV in 2 + 1 dimensions) at positive energy. In addition, we are focused on a family of reflectionless (transparent) potentials parameterized by a function of two variables. In particular, we show that there are no isolated soliton type waves in the large time asymptotics for these solutions in contrast with well-known large time asymptotics for solutions of the KdV equation with reflectionless initial data.

References in corpus (1)

• Transparent Potentials at Fixed Energy in Dimension Two. Fixed-Energy Dispersion Relations for the Fast Decaying Potentials

Cited by in corpus (4)

• Miura Maps and Inverse Scattering for the Novikov-Veselov Equation
• A large time asymptotics for the solution of the Cauchy problem for the Novikov-Veselov equation at negative energy with non-singular scattering data
• Numerical study of blow-up and stability of line solitons for the Novikov-Veselov equation
• Absence of sufficiently localized traveling wave solutions for the Novikov-Veselov equation at zero energy