24 citations · 84 across the 13 of their papers we have counts for
8 papers · 1 filter
Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation. II
Anna Kazeykina, Claudio Muñoz
In this paper we continue our study on the Cauchy problem for the two-dimensional Novikov-Veselov (NV) equation, integrable via the inverse scattering transform for the two dimensi…
Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation
Anna Kazeykina, Claudio Muñoz
We consider the Cauchy problem for the two-dimensional Novikov-Veselov equation integrable via the inverse scattering problem for the Schrödinger operator with fixed negative energ…
Absence of sufficiently localized traveling wave solutions for the Novikov-Veselov equation at zero energy
Anna Kazeykina
We demonstrate that the Novikov.Veselov equation (a (2+1)-dimensional analog of KdV) at zero energy does not possess solitons with the space localization stronger than O(|x|^{-4}).
Absence of solitons with sufficient algebraic localization for the Novikov-Veselov equation at nonzero energy
Anna Kazeykina
We show that the Novikov--Veselov equation (an analog of KdV in dimension 2 + 1) at positive and negative energies does not have solitons with the space localization stronger than…
A large time asymptotics for the solution of the Cauchy problem for the Novikov-Veselov equation at negative energy with non-singular scattering data
Anna Kazeykina
In the present paper we are concerned with the Novikov--Veselov equation at negative energy, i.e. with the --dimensional analog of the KdV equation integrable by the met…
Large time asymptotics for the Grinevich-Zakharov potentials
Anna Kazeykina, Roman Novikov
In this article we show that the large time asymptotics for the Grinevich-Zakharov rational solutions of the Novikov-Veselov equation at positive energy (an analog of KdV in 2+1 di…
A large time asymptotics for transparent potentials for the Novikov-Veselov equation at positive energy
Anna Kazeykina, Roman Novikov
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 dimensi…
Absence of exponentially localized solitons for the Novikov-Veselov equation at positive energy
Roman Novikov
In this note we show that the Novikov-Veselov equation at positive energy (an analog of KdV in 2+1 dimensions) has no exponentially localized solitons ( in the two-dimensional sens…