Adilkhanov, A.N.Taimanov, I.A.2017-12-202017-12-202017-01-01A.N. Adilkhanov, I.A. Taimanov, On numerical study of the discrete spectrum of a two-dimensional Schrödinger operator with soliton potential, In Communications in Nonlinear Science and Numerical Simulation, Volume 42, 2017, Pages 83-9210075704https://www.sciencedirect.com/science/article/pii/S1007570416301356http://nur.nu.edu.kz/handle/123456789/2956Abstract The discrete spectra of certain two-dimensional Schrödinger operators are numerically calculated. These operators are obtained by the Moutard transformation and have interesting spectral properties: their kernels are multi-dimensional and the deformations of potentials via the Novikov–Veselov equation (a two-dimensional generalization of the Korteweg–de Vries equation) lead to blowups. The calculations supply the numerical evidence for some statements about the integrable systems related to a 2D Schrödinger operator. The numerical scheme is applicable to a general 2D Schrödinger operator with fast decaying potential.enSchrodinger operatorDiscrete spectrumGalerkin methodSoliton,Article© 2016 Elsevier B.V. All rights reserved.