HOLOMORPHIC BUNDLES OVER ALGEBRAIC CURVES AND NON-LINEAR EQUATIONS
From MaRDI portal
Publication:3341309
DOI10.1070/RM1980v035n06ABEH001974zbMath0548.35100MaRDI QIDQ3341309
S. P. Novikov, I. M. Krichever
Publication date: 1980
Published in: Russian Mathematical Surveys (Search for Journal in Brave)
inverse scattering methodexact solutions depending on functional parametersfinite- zone solutions of Kadomtsev-Petviashvili equationsmulti-point vector-valued analogue of Baker-Akhiezer functionmultidimensional holomorphic bundles
Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Nonlinear first-order PDEs (35F20) Partial differential equations of mathematical physics and other areas of application (35Q99) Solutions to PDEs in closed form (35C05) Analytic spaces (32C99)
Related Items (65)
Vector addition theorems and Baker-Akhiezer functions ⋮ Hierarchies of finite-dimensional Lax equations with a spectral parameter on a Riemann surface and semisimple Lie algebras ⋮ The AKNS hierarchy and finite-gap Schrödinger potentials ⋮ The Krichever map, vector bundles over algebraic curves, and Heisenberg algebras ⋮ Symmetry reductions and traveling wave solutions for the Krichever-Novikov equation ⋮ The discrete Korteweg-de Vries equation ⋮ Darboux transformations for higher-rank Kadomtsev-Petviashvili and Krichever-Novikov equations ⋮ Alternative proof of Mironov's results on commuting self-adjoint operators of rank 2 ⋮ Isospectral Hamiltonian flows in finite and infinite dimensions. II: Integration of flows ⋮ Solutions of the KP equation associated to rank-three commuting differential operators over a singular elliptic curve ⋮ Abelian integrals and the reduction method for an integrable Hamiltonian system ⋮ Commuting pairs of linear ordinary differential operators of orders four and six ⋮ Classical and quantum integrable systems in \(\widetilde{\mathfrak gl}(2)^{+*}\) and separation of variables ⋮ Isospectral Hamiltonian flows in finite and infinite dimensions. I: Generalized Moser systems and moment maps into loop algebras ⋮ Lie group analysis of a generalized Krichever-Novikov differential-difference equation ⋮ Integrable systems and algebraic surfaces ⋮ On Lie algebras responsible for integrability of \((1+1)\)-dimensional scalar evolution PDEs ⋮ Matrix divisors on Riemann surfaces and Lax operator algebras ⋮ Solutions of Adler's Lattice Equation Associated with 2-Cycles of the Bäcklund Transformation ⋮ Lie algebras responsible for zero-curvature representations of scalar evolution equations ⋮ Quasiperiodic solutions for matrix nonlinear Schrödinger equations ⋮ Negative flows of generalized KdV and mKdV hierarchies and their gauge-Miura transformations ⋮ On a coupled Kadomtsev–Petviashvili system associated with an elliptic curve ⋮ Negative flows for several integrable models ⋮ Semisimple Lie algebras and Hamiltonian theory of finite-dimensional Lax equations with spectral parameter on a Riemann surface ⋮ On nonlocal symmetries for the Krichever-Novikov equation ⋮ Elliptic solutions of Boussinesq type lattice equations and the elliptic \(N\)th root of unity ⋮ Computational and numerical solutions for \((2+1)\)-dimensional integrable Schwarz-Korteweg-de Vries equation with Miura transform ⋮ Discretization of commuting ordinary differential operators of rank 2 in the case of elliptic spectral curves ⋮ On commuting differential operators of rank 2 ⋮ New solutions of the Schwarzian Korteweg-de Vries equation in \(2+1\) dimensions based on weak symmetries ⋮ On the eigenfunctions of the one-dimensional Schrödinger operator with a polynomial potential ⋮ On commuting differential operators with polynomial coefficients corresponding to spectral curves of genus one ⋮ Commuting differential operators of rank 2 with trigonometric coefficients ⋮ Lax systems and nonlinear equations on a time-space scale ⋮ Differential substitutions for non-Abelian equations of KdV type ⋮ Commuting Krichever-Novikov differential operators with polynomial coefficients ⋮ Conditions for the existence of higher symmetries of evolutionary equations on the lattice ⋮ Almost periodic solutions of a \((2+1)\)-dimensional Schwarzian Korteweg de Vries equation ⋮ Algebraic-geometric solutions of the Krichever-Novikov equation ⋮ Multiple solutions for the Schwarzian Korteweg-de Vries equation in \((2+1)\) dimensions ⋮ Multipotentialisations and Iterating-Solution Formulae: The Krichever–Novikov Equation ⋮ Compatible Hamiltonian operators for the Krichever-Novikov equation ⋮ Field theory generalizations of two-body Calogero-Moser models in the form of Landau-Lifshitz equations ⋮ Coverings and fundamental algebras for partial differential equations ⋮ The exp-function approach to the Schwarzian Korteweg-de Vries equation ⋮ Difference Krichever-Novikov operators of rank 2 ⋮ Poisson groups and differential Galois theory of Schrödinger equation on the circle ⋮ Fourth-order recursion operators for third-order evolution equations ⋮ Commuting ordinary differential operators and the Dixmier test ⋮ Remarks on KdV-type flows on star-shaped curves ⋮ A family of integrable evolution equations of third order ⋮ Algebro-geometric integration of the Q1 lattice equation via nonlinear integrable symplectic maps ⋮ A variational perspective on continuum limits of ABS and lattice GD equations ⋮ A class of integrable flows on the space of symmetric matrices ⋮ On the recursion operators for integrable equations ⋮ Commuting elements in the first Weyl algebra over \(\mathbb{Q} \) ⋮ Cayley-Hamilton theorem, vector bundles and divisors of commuting operators ⋮ Families of orthogonal Laurent polynomials, hyperelliptic lie algebras and elliptic integrals ⋮ Algebraic solutions of the multicomponent KP hierarchy ⋮ A review of recent work on almost periodic differential and difference operators ⋮ Separation of variables for soliton equations via their binary constrained flows ⋮ Darboux coordinates and Liouville-Arnold integration in loop algebras ⋮ A computational approach to soliton solutions of the Kadomtsev-Petviashvili equation ⋮ Finite-dimensional coadjoint orbits in loop algebras
This page was built for publication: HOLOMORPHIC BUNDLES OVER ALGEBRAIC CURVES AND NON-LINEAR EQUATIONS
