TY  - JOUR
ID  - Hwang2022
LB  - Hwang2022
AU  - Hwang, Guenbo
AU  - Moon, Byungsoo
TI  - The d-bar formalism for the modified Veselov-Novikov equation on the half-plane
ST  - The d-bar formalism for the modified Veselov-Novikov equation on the half-plane
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2022
VL  - 42
IS  - 2
SP  - 179
EP  - 217
DO  - https://doi.org/10.7494/OpMath.2022.42.2.179
UR  - https://doi.org/10.7494/OpMath.2022.42.2.179
AB  - We study the modified Veselov-Novikov equation (mVN) posed on the half-plane via the Fokas method, considered as an extension of the inverse scattering transform for boundary value problems. The mVN equation is one of the most natural \((2+1)\)-dimensional generalization of the \((1+1)\)-dimensional modified Korteweg-de Vries equation in the sense as to how the Novikov-Veselov equation is related to the Korteweg-de Vries equation. In this paper, by means of the Fokas method, we present the so-called global relation for the mVN equation, which is an algebraic equation coupled with the spectral functions, and the \(d\)-bar formalism, also known as Pompieu's formula. In addition, we characterize the \(d\)-bar derivatives and the relevant jumps across certain domains of the complex plane in terms of the spectral functions.
KW  - initial-boundary value problem
KW  - integrable nonlinear PDE
KW  - spectral analysis
KW  - \(d\)-bar
SN  - 1232-9274
ER  -