Abstract:
Complete solutions of the commutation equations of ordinary differential operators are obtained, to which there corresponds a three-dimensional vector bundle of common eigenfunctions over an elliptic curve. The deformation of the commuting pair by the Kadomtsev–Petviashvili equation is studied. The finite-zone solutions of the Kadomtsev–Petviashvili equation of rank 3 and genus 1 are explicitly expressed in terms of functional parameters satisfying a Boussinesq-type system of two evolution equations.
Bibliography: 40 titles.
This publication is cited in the following 40 articles:
J. Guo, A. Zheglov, “On Some Questions around Berest's Conjecture”, Math. Notes, 116:2 (2024), 238–251
Leonid Makar-Limanov, “Centralizers of Rank One in the First Weyl Algebra”, SIGMA, 17 (2021), 052, 13 pp.
Gulnara S. Mauleshova, Andrey E. Mironov, “Discretization of Commuting Ordinary Differential Operators of Rank 2 in the Case of Elliptic Spectral Curves”, Proc. Steklov Inst. Math., 310 (2020), 202–213
Emma Previato, Sonia L. Rueda, Maria-Angeles Zurro, “Commuting Ordinary Differential Operators and the Dixmier Test”, SIGMA, 15 (2019), 101, 23 pp.
Vardan Oganesyan, “Matrix Commuting Differential Operators of Rank 2 and Arbitrary Genus”, International Mathematics Research Notices, 2019:3 (2019), 834
V. S. Oganesyan, “Commuting Differential Operators of Rank 2 with Rational Coefficients”, Funct. Anal. Appl., 52:3 (2018), 203–213
V. S. Oganesyan, “Alternative proof of Mironov's results on commuting self-adjoint operators of rank 2”, Siberian Math. J., 59:1 (2018), 102–106
V. S. Oganesyan, “The AKNS hierarchy and finite-gap Schrödinger potentials”, Theoret. and Math. Phys., 196:1 (2018), 983–995
Igor Burban, Alexander Zheglov, “Fourier–Mukai transform on Weierstrass cubics and commuting differential operators”, Int. J. Math., 29:10 (2018), 1850064
D. A. Pogorelov, A. B. Zheglov, “An algorithm for construction of commuting ordinary differential operators by geometric data”, Lobachevskii J Math, 38:6 (2017), 1075
V. S. Oganesyan, “Common Eigenfunctions of Commuting Differential Operators of Rank 2”, Math. Notes, 99:2 (2016), 308–311
V. S. Oganesyan, “Commuting Differential Operators of Rank 2 with Polynomial Coefficients”, Funct. Anal. Appl., 50:1 (2016), 54–61
V. S. Oganesyan, “On operators of the form ∂4x+u(x) from a pair of commuting differential operators of rank 2 and genus g”, Russian Math. Surveys, 71:3 (2016), 591–593
A. E. Mironov, “Self-adjoint commuting differential operators of rank two”, Russian Math. Surveys, 71:4 (2016), 751–779
A. B. Zheglov, A. E. Mironov, B. T. Saparbayeva, “Commuting Krichever–Novikov differential operators with polynomial coefficients”, Siberian Math. J., 57:5 (2016), 819–823
Vardan Oganesyan, “Explicit Characterization of Some Commuting Differential Operators of Rank 2”, Int Math Res Notices, 2016, rnw085
N Delice, F.W. Nijhoff, S Yoo-Kong, “On elliptic Lax systems on the lattice and a compound theorem for hyperdeterminants”, J. Phys. A: Math. Theor, 48:3 (2015), 035206
V. S. Oganesyan, “Commuting differential operators of rank 2 and arbitrary genus g with polynomial coefficients”, Russian Math. Surveys, 70:1 (2015), 165–167
V. N. Davletshina, “Self-Adjoint Commuting Differential Operators of Rank 2 and Their Deformations Given by Soliton Equations”, Math. Notes, 97:3 (2015), 333–340
A. E. Mironov, B. T. Saparbayeva, “On the eigenfunctions of the one-dimensional Schrödinger operator with a polynomial potential”, Dokl. Math, 91:2 (2015), 171
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