Rational and elliptic solutions of the korteweg-de vries equation and a related many-body problem
From MaRDI portal
Publication:4106928
DOI10.1002/cpa.3160300106zbMath0338.35024OpenAlexW2003485783MaRDI QIDQ4106928
Hélène Airault, H. P. jun. McKean, Jürgen K. Moser
Publication date: 1977
Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/cpa.3160300106
Related Items
Spectral characteristics of elliptic solitons, Algebraic integrability for the Schrödinger equation and finite reflection groups, Singular solutions of the KdV equation and the inverse scattering method, Darboux theorems and Wronskian formulas for integrable systems. I: Constrained KP flows, Dynamics of the Calogero-Moser system and the reduction of hyperelliptic integrals of elliptic integrals, A new class of integrable systems and its relation to solitons, Chaotic perturbations of KdV. I. Rational solutions, Elliptic solutions of nonlinear integrable equations and related topics, On the geometry of elliptic solitons, Reduction of theta functions and elliptic finite-gap potentials, On the two-gap elliptic potentials, Finite-gap elliptic solutions of the KdV equation, Quasi-periodic solutions to the hierarchy of four-component Toda lattices, The structure of the rational solutions to the Boussinesq equation, Multi-particle dynamical systems and polynomials, The discrete Korteweg-de Vries equation, A survey on Huygens' principle, Picard potential and Hill's equation on a torus, Action-angle maps and scattering theory for some finite-dimensional integrable systems. I: The pure soliton case, Classical scattering theory in one dimension, The long wave limiting of the discrete nonlinear evolution equations, Special polynomials associated with rational solutions of the Painlevé equations and applications to soliton equations, Multiscale \(N=2\) SUSY field theories, integrable systems and their stringy/brane origin, Comments on ``Two exact solutions to the general relativistic Binet's equation, Soliton, rational and special solutions of the Korteweg-de Vries hierarchy, Algebraic aspects of nonlinear differential equations, Complex solitons and poles of the sine-Gordon equation, The master \(T\)-operator for the Gaudin model and the KP hierarchy, On a class of polynomials connected with the Korteweg-de Vries equation, Monodromy- and spectrum-preserving deformations. I, Singular solutions of the equation (d'Alembert operator) \(\phi+(m^ 2/2)\exp \phi=0\) and dynamics of singularities, On the integrable variant of the Boussinesq system: Painlevé property, rational solutions, a related many-body system, and equivalence with the AKNS hierarchy, A noncommutative version of the bispectral problem., Remarks on the Yablonskii-Vorob'ev polynomials, Elliptic solutions of the Kadomtsev-Petviashvili equation and integrable systems of particles, Perfectly invisible \( \mathcal{P}\mathcal{T} \)-symmetric zero-gap systems, conformal field theoretical kinks, and exotic nonlinear supersymmetry, Tangential polynomials and elliptic solitons, Elliptic traveling waves of the Olver equation, \(\mathcal D\)-bundles and integrable hierarchies, Geometrical loci and cfts via the Virasoro symmetry of the mKdV-SG hierarchy: an excursus, Elliptic solutions of the Korteweg-de Vries equation, Construction of isospectral deformations of differential operators with periodic coefficients, On the Moutard transformation and its applications to spectral theory and soliton equations, Decomposition of a \(2 + 1\)-dimensional Volterra type lattice and its quasi-periodic solutions, The generalized Neumann hierarchy associated with the energy dependent Schrödinger equation, Differential equations in the spectral parameter, Darboux transformations and a hierarchy of master symmetries for KdV, Nonlinear symmetries of perfectly invisible \textit{PT}-regularized conformal and superconformal mechanics systems, A note on the quasi-periodic solutions of the modified Boussinesq hierarchy, Relations satisfied by point vortex equilibria with strength ratio $-2$, Rational solutions of nonlinear evolution equations, vertex operators, and bispectrality, Finite-band solutions for the hierarchy of coupled Toda lattices, Application of the trigonal curve to the Blaszak-Marciniak lattice hierarchy, Rational \(KP\) and \(mKP\)-solutions in Wronskian form, Nonlinear evolution equations and hyperelliptic covers of elliptic curves, Clustered equilibria of point vortices, On Darboux-Treibich-Verdier potentials, On complete integrability of a hierarchy of finite-dimensional Hamiltonian systems, Rational solutions of the Toda lattice equation in Casoratian form, On a class of solutions of KdV, Periodic finite-genus solutions of the KdV equation are orbitally stable, Ideals of rings of differential operators on algebraic curves (with an appendix by George Wilson)., \(N\)-soliton solution and its Wronskian form of a \((3+1)\)-dimensional nonlinear evolution equation, On ``new travelling wave solutions of the KdV and the KdV-Burgers equations, Differential equations in the spectral parameter, Periodic billiard orbits on \(n\)-dimensional ellipsoids with impacts on confocal quadrics and isoperiodic deformations, Algebro-geometric constructions of the modified Boussinesq flows and quasi-periodic solutions, Hankel determinant approach to generalized Vorob'ev-Yablonski polynomials and their roots, Two-dimensional rational solitons and their blowup via the Moutard transformation, Self-similar solutions of the Korteweg-de Vries equation and potentials with a trivial s-matrix, A second Wronskian formulation of the Boussinesq equation, Geometry of KdV. IV: Abel sums, Jacobi variety, and theta function in the scattering case, The continuation method for rational and deficient systems, On a class of elliptic solutions of the Boussinesq equations, A characterization of all elliptic algebro-geometric solutions of the AKNS hierarchy, Solutions of the Boussinesq equation, An analytical solution for a coupled partial differential equation, Chaotic perturbations of KdV equations. I: Rational solutions, Spin Calogero particles and bispectral solutions of the matrix KP hierarchy, On the periodic KdV equation in weighted Sobolev spaces, Hirota equation and Bethe ansatz, Rational solutions of the classical Boussinesq system, The elliptic-in-\(t\) solutions of the nonlinear Schrödinger equation, On a complete solution of the quantum Dell system, The inverse periodic problem for Hill's equation with a finite-gap potential, Reflectionless Schrödinger operators, the dynamics of zeros, and the solitonic Sato formula, \(q\)-KP hierarchy, bispectrality and Calogero-Moser systems, Hidden hierarchies of KdV type on Birkhoff strata, Rational solutions of the Zakharov-Shabat equations and completely integrable systems of \(N\) particles on a line, An elementary approach to the polynomial \(\tau\)-functions of the KP-hierarchy, Similarity, Bäcklund transformations and rational solutions, On a theorem of Halphen and its application to integrable systems, Dynamics of the singularities of solutions of some nonlinear equations, Singular phases of Seiberg-Witten integrable systems: weak and strong coupling, Application of inverse scattering method to singular solutions of nonlinear equations. I, Constrained KP hierarchy and bi-Hamiltonian structures, Extension of the class of integrable dynamical systems connected with semisimple Lie algebras, The Fredholm determinant method for the KdV equations, Some nonlinear evolution equations and related topics arising in medical imaging, A generalisation of the Calogero-Moser system, Loop groups and equations of KdV type, ALGEBRO-GEOMETRIC SOLUTIONS OF THE BOUSSINESQ HIERARCHY, Constrained Toda hierarchy and turning points of the Ruijsenaars-Schneider model, The Painlevé Property and Hirota's Method, Integrable Hamiltonian systems related to the polynomial eigenvalue problem, Rational Ruijsenaars-Schneider hierarchy and bispectral difference operators, Classification of KPI lumps, Integrable nonlinear evolution equations and dynamical systems in multidimensions, Characterization of rational solutions of a KdV-like equation, Dynamics of poles of elliptic solutions to the BKP equation, Action-angle maps and scattering theory for some finite-dimensional integrable systems. III: Sutherland type systems and their duals, Treibich-Verdier potentials and the stationary (m)KdV hierarchy, Analytic Riemann Theta Function Solutions of Coupled Korteweg-de Vries Hierarchy, Extended tanh-function method and its applications to nonlinear equations, Finite dimensional Kadomtsev-Petviashvili τ-functions. I. Finite Grassmannians, The inverse scattering transform for the KdV equation with step-like singular Miura initial profiles, Bispectral KP solutions and linearization of Calogero-Moser particle systems, The constraints of potentials and the finite-dimensional integrable systems, A hierarchy of long wave-short wave type equations: quasi-periodic behavior of solutions and their representation, The Riemann theta function solutions for the hierarchy of Bogoyavlensky lattices, Trigonal curves and algebro-geometric solutions to soliton hierarchies I, Elliptic soliton solutions: \(\tau\) functions, vertex operators and bilinear identities, A turbulence model with stochastic soliton motion, Classical Liouville completely integrable systems associated with the solutions of Boussinesq–Burgers’ hierarchy, The fourth Painlevé equation and associated special polynomials, Integrable time-discretization of the Ruijsenaars-Schneider model, Integrable many-body systems in the field theories, Solutions of the KdV equation elliptic in \(t\), A Bochner type characterization theorem for exceptional orthogonal polynomials, Spin generalization of the Calogero–Moser hierarchy and the matrix KP hierarchy, Orbital bifurcations and shoaling of cnoidal waves, Time-band limiting matrices and lamé's equation, Constraints of the Kadomtsev–Petviashvili hierarchy, Zeros of Wronskians of Hermite polynomials and Young diagrams, KP hierarchy for the cyclic quiver, Matrix Kadomtsev-Petviashvili hierarchy and spin generalization of trigonometric Calogero-Moser hierarchy, The coupled Sasa–Satsuma hierarchy: Trigonal curve and finite genus solutions, Rational solutions of the Kadomtsev–Petviashvili hierarchy and the dynamics of their poles. I. New form of a general rational solution, Calogero–Moser hierarchy and KP hierarchy, Elliptic solutions and blow-up in an integrable Hénon–Heiles system, Multi-lump wave patterns of KPI via integer partitions, Multivortex Traveling Waves for the Gross--Pitaevskii Equation and the Adler--Moser Polynomials, Elliptic solutions of Boussinesq type lattice equations and the elliptic \(N\)th root of unity, New integrable nonlinear integrodifferential equations and related solvable finite-dimensional dynamical systems, Elliptic solutions of the semidiscrete B-version of the Kadomtsev-Petviashvili equation, A time-discretized version of the Calogero-Moser model, An explicit formula for a class of solutions of the KdV equation, Hamiltonian systems of Calogero-type, and two-dimensional Yang-Mills theory, Degenerate Riemann theta functions, Fredholm and Wronskian representations of the solutions to the KdV equation and the degenerate rational case, Closed geodesics and billiards on quadrics related to elliptic KdV solutions, 3-tangential polynomials and \(t\)-periodic solutions of the KdV equation, The Lagnese-Stellmacher potentials revisited, Highest weight modules over the \(W_{1+\infty}\) algebra and the bispectral problem, KP hierarchy and trigonometric Calogero–Moser hierarchy, Quasiperiodic and periodic solutions for vector nonlinear Schrödinger equations, Singular sector of the Kadomtsev–Petviashvili hierarchy, ∂̄ operators of nonzero index, and associated integrable systems, Equivalence of Third‐Order Ordinary Differential Equations to Chazy Equations I–XIII, A transformation between stationary point vortex equilibria, The application of the theory of trigonal curves to the discrete coupled nonlinear Schrödinger hierarchy, Explicit quasi-periodic solutions of the Vakhnenko equation, Higher-order rational solitons and rogue-like wave solutions of the \((2+1)\)-dimensional nonlinear fluid mechanics equations, Huygens' principle, Dirac operators, and rational solutions of the AKNS hierarchy, Huygens' principle for hyperbolic operators and integrable hierarchies, Solitons and almost-intertwining matrices, Properties of the Benjamin–Ono equation, Rational solutions of the (2+1)-dimensional Kaup-Kupershmidt equation, Singular fiber of the Mumford system and rational solutions to the KdV hierarchy, Counting monster potentials, Geometry of Calogero-Moser systems, Algebro-geometric solutions of the coupled modified Korteweg-de Vries hierarchy, Algebro-geometric integration of the modified Belov-Chaltikian lattice hierarchy, Liouville chains: new hybrid vortex equilibria of the two-dimensional Euler equation, Rational solutions of the KP hierarchy and the dynamics of their poles. II. Construction of the degenerate polynomial solutions, Cusps and 𝒟-modules, Elliptic solutions of the Toda lattice hierarchy and the elliptic Ruijsenaars-Schneider model, On algebro-geometric simply-periodic solutions of the KdV hierarchy, Kadomtsev-Petviashvili turning points and CKP hierarchy, The expansions of spectral function and the corresponding finite dimensional integrable systems, On the rational monodromy-free potentials with sextic growth, Spatial Analyticity of Solutions to Integrable Systems. I. The KdV Case, Integrability, conservation laws and solitons of a many-body dynamical system associated with the half-wave maps equation, TEMPORAL EVOLUTIONS AND STATIONARY WAVES FOR PERTURBED KDV EQUATION WITH NONLOCAL TERM, Exact solutions for a class of integrable Hénon–Heiles-type systems, Elliptic solutions to matrix KP hierarchy and spin generalization of elliptic Calogero–Moser model, Rational KdV potentials and differential Galois theory, Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies - an analytic approach, Elliptic solutions to integrable nonlinear equations and many-body systems, Commuting integral and differential operators and the master symmetries of the Korteweg–de Vries equation, Canonical Systems with Rational Spectral Densities: Explicit Formulas and Applications, Hyperelliptic $d$-osculating covers and rational surfaces, A particle representation for Korteweg–de Vries solitons, Calogero-Moser spaces and an adelic \(W\)-algebra., The geometry of Calogero-Moser systems., On the heat kernel and the Korteweg-de Vries hierarchy., Finite heat kernel expansions on the real line, Soliton Theory and Hankel Operators, On classes of integrable systems and the Painlevé property, The Painlevé property and Bäcklund transformations for the sequence of Boussinesq equations, Field analogue of the Ruijsenaars-Schneider model, Unnamed Item, A New Approach to the Boussinesq Hierarchy, Deformed Calogero-Moser operators and ideals of rational Cherednik algebras, On solutions to a novel non-evolutionary integrable 1 + 1 PDE, On integrability of the deformed Ruijsenaars-Schneider system, Reflective prolate‐spheroidal operators and the adelic Grassmannian, Polynomial sequences related to point vortex equilibria with three strengths, Elliptic solutions of the Toda lattice with constraint of type B and deformed Ruijsenaars-Schneider system, Periodic solutions of the non-chiral intermediate Heisenberg ferromagnet equation described by elliptic spin Calogero-Moser dynamics, Elliptic KdV potentials and conical metrics of positive constant curvature. I, Lower bounds on the radius of spatial analyticity for the higher order nonlinear dispersive equation on the real line, A focusing-defocusing intermediate nonlinear Schrödinger system, Application of the trigonal curve to a hierarchy of generalized Toda lattices, On the integrable symplectic map and the \(N\)-soliton solution of the Toda lattice, Monodromy free linear equations and many-body systems, Higher-order heat equation and the Gelfand-Dickey hierarchy, Abelian pole systems and Riemann-Schottky-type problems, Quasi-periodic solutions of the Belov–Chaltikian lattice hierarchy, Time discretization of the spin Calogero-Moser model and the semi-discrete matrix KP hierarchy, Note on nonlinear Schrödinger equation, KdV equation and 2D topological Yang–Mills–Higgs theory, Elliptic families of solutions to constrained Toda hierarchy, An explicit characterization of Calogero–Moser systems, Elliptic (N, N′)-soliton solutions of the lattice Kadomtsev-Petviashvili equation, Hidden local, quasi-local and non-local symmetries in integrable systems., Abelian solitons, Supersymmetric Calogero-Moser-Sutherland models and Jack superpolynomials, Three kinds of constraints of potential for KdV hierarchy, Bundle bispectrality for matrix differential equations., A Connection Between Geometry and Dynamical Systems, Rational Solutions of Painlevé Equations, RATIONAL SOLUTIONS OF THE BOUSSINESQ EQUATION, Three-sheeted Riemann surface and solutions of the Itoh–Narita–Bogoyavlensky lattice hierarchy, Multi-solitons of the half-wave maps equation and Calogero–Moser spin–pole dynamics, Toda lattice hierarchy and trigonometric Ruijsenaars–Schneider hierarchy, Elliptic solutions to the KP hierarchy and elliptic Calogero–Moser model
Cites Work
