Scattering and inverse scattering for first order systems

From MaRDI portal
Publication:3660113

DOI10.1002/cpa.3160370105zbMath0514.34021OpenAlexW1993232980MaRDI QIDQ3660113

Richard W. Beals, Ronald R. Coifman

Publication date: 1984

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/cpa.3160370105



Related Items

Inverse problem for the Rayleigh system with spectral data, The asymptotic stability of solitons for the focusing mKdV equation with weak weighted Sobolev initial data, The Riemann–Hilbert approach to the generalized second-order flow of three-wave hierarchy, On the distribution of the length of the longest increasing subsequence of random permutations, Hamiltonian Hierarchies on Semisimple Lie Algebras, Long-time asymptotics for the pure radiation solution of the sine—gordon equation, The Schrödinger equation and a multidimensional inverse scattering transform, An inverse spectral problem for differential systems on the half-line with multiplied roots of the characteristic polynomial, On nontrivial interactions and complete integrability of soliton equations, R-matrices and higher Poisson brackets for integrable systems, A steepest descent method for oscillatory Riemann-Hilbert problems, Inverse scattering on the half-line for generalized ZS-AKNS system with general boundary conditions, Inverse Scattering Transform and Soliton Solutions for the Hirota Equation with $N$ Distinct Arbitrary Order Poles, Bäcklund Transformations and Inverse Scattering Solutions for Some Pseudospherical Surface Equations, Long-time asymptotics for the spin-1 Gross-Pitaevskii equation, Inverse scattering on the half-line for a first-order system with a general boundary condition, Spectral analysis for differential systems with a singularity, On the Dissipative Evolution Equations Associated with the Zakharov-Shabat System with a Quadratic Spectral Parameter, Riemann-Hilbert method and multi-soliton solutions of an extended modified Korteweg-de Vries equation with \(N\) distinct arbitrary-order poles, Riemann-Hilbert problem for the focusing nonlinear Schrödinger equation with multiple high-order poles under nonzero boundary conditions, On the Caudrey-Beals-Coifman System and the Gauge Group Action, Asymptotic stability of N-solitons in the cubic NLS equation, Global conservative solutions of the nonlocal NLS equation beyond blow-up, Nonlinear systems related to an arbitrary space–time dependence of the spectral transform, Completeness of the eigenfunctions for the Caudrey–Beals–Coifman system, \(l^2\)-Sobolev space bijectivity of the scattering-inverse scattering transforms related to defocusing Ablowitz-Ladik systems, Nonlinear evolution equations related to Kac-Moody algebras $A_r^{(1)}$: spectral aspects, A Riemann-Hilbert approach to Fredholm determinants of Hankel composition operators: scalar-valued kernels, On the Cauchy problem of defocusing mKdV equation with finite density initial data: long time asymptotics in soliton-less regions, Soliton versus the gas: Fredholm determinants, analysis, and the rapid oscillations behind the kinetic equation, Global existence for the derivative nonlinear Schrödinger equation by the method of inverse scattering, Long-time asymptotics of the coupled modified Korteweg-de Vries equation, Long time asymptotic behavior for the nonlocal mKdV equation in solitonic space-time regions, A Riemann–Hilbert approach to the modified Camassa–Holm equation with nonzero boundary conditions, Inverse scattering transformation for the \(N\)-component focusing nonlinear Schrödinger equation with nonzero boundary conditions, Three Lectures on “Fifty Years of KdV: An Integrable System”, Benjamin-Ono and Intermediate Long Wave Equations: Modeling, IST and PDE, Inverse Scattering and Global Well-Posedness in One and Two Space Dimensions, Inverse Scattering for the Massive Thirring Model, Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory, Unnamed Item, Symmetries and Integrability, Evolution of Weyl Functions and Initial-Boundary Value Problems, Asymptotics behavior for the integrable nonlinear Schrödinger equation with quartic terms: Cauchy problem, Asymptotics of Solutions of Some Integral Equations Connected with Differential Systems with a Singularity, Focusing nonlinear Schrödinger equation with infinitely many solitons, Solution of three waves interaction type models with nontrivial asymptotic and boundary conditions, The inverse boundary problem for the Rayleigh system, Modified nonlinear Schrödinger equation: Spectral transform and N-soliton solution, Inverse scattering problem for anisotropic media, Strong regularizing effect of integrable systems, Long time asymptotics behavior of the focusing nonlinear Kundu-Eckhaus equation, Some features of the maps from potential to spectral data, Classification of stroke using neural networks in electrical impedance tomography, L 2-Sobolev space bijectivity of the inverse scattering of a 3 × 3 AKNS system, Global well-posedness for the derivative non-linear Schrödinger equation, An example of ∂̄ problem arising in a finite difference context: Direct and inverse problem for the discrete analog of the equation ψx x+uψ=σψy, On the Long-Time Asymptotic Behavior of the Modified Korteweg--de Vries Equation with Step-like Initial Data, Riemann-Hilbert factorization of matrices invariant under inversion in a circle, The symmetries of solitons, Inverse scattering problems for the Landau-Lifschitz equations, On the integrability of linear and nonlinear partial differential equations, Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions, The asymptotic stability of solitons in the cubic NLS equation on the line, Pseudo-Hermitian Reduction of a Generalized Heisenberg Ferromagnet Equation. I. Auxiliary System and Fundamental Properties, Semiclassical Limit of Focusing NLS for a Family of Square Barrier Initial Data, Correspondence theorems for hierarchies of equations of pseudo-spherical type, Hamiltonian structure for degenerate AKNS systems, The periodic Euler-Bernoulli equation, IST Versus PDE: A Comparative Study, An inverse problem for the non-selfadjoint matrix Sturm–Liouville equation on the half-line, Uniqueness in a frequency-domain inverse problem of a stratified uniaxial bianisotropic medium., Initial-Boundary Value Problems for the Coupled Nonlinear Schrödinger Equation on the Half-Line, LONG-TIME ASYMPTOTICS OF THE TODA LATTICE FOR DECAYING INITIAL DATA REVISITED, The \(N\)-wave equations with \(\mathcal{PT}\) symmetry, The Cauchy problem of the Ward equation with mixed scattering data, Inverse Scattering Transform for the Multi-Component Nonlinear Schrödinger Equation with Nonzero Boundary Conditions, High-temperature analysis of the transverse dynamical two-point correlation function of the XX quantum-spin chain, STRINGS, WAVES, DRUMS: SPECTRA AND INVERSE PROBLEMS, The derivative nonlinear Schrödinger equation: Global well-posedness and soliton resolution, Long-Time Asymptotics for the Nonlocal MKdV Equation*, Asymptotics of oscillatory Riemann–Hilbert problems, CBC Systems with Mikhailov Reductions by Coxeter Automorphism: I. Spectral Theory of the Recursion Operators, High‐Order Soliton Solution of Landau–Lifshitz Equation, On the origins of Riemann–Hilbert problems in mathematics*, Application of the Nonlinear Steepest Descent Method to the Coupled Sasa-Satsuma Equation, Painlevé analysis of the damped, driven nonlinear Schrödinger equation, Inverse Scattering and the Bäcklund Transformation for the Generalized Wave and Generalized Sine‐Gordon Equations, Higher order asymptotics of the modified non-linear schrödinger equation, On the recursion operators for the Gerdjikov, Mikhailov, and Valchev system, Twisted hierarchies associated with the generalized sine-Gordon equation, Inverse Scattering Transform for the Defocusing Manakov System with Nonzero Boundary Conditions, Long-time asymptotic behavior for the Gerdjikov-Ivanov type of derivative nonlinear Schrödinger equation with time-periodic boundary condition, Long-time asymptotics of the periodic Toda lattice under short-range perturbations, The generalised Zakharov–Shabat system and the gauge group action, Nonlocal symmetries and the Kaup–Kupershmidt equation, Inverse Scattering Transform for the Defocusing Manakov System with Non-Parallel Boundary Conditions at Infinity, A twisted integrable hierarchy with $\mathbb D_2$D2 symmetry, From Painlevé to Zakharov–Shabat and beyond: Fredholm determinants and integro-differential hierarchies, Nonlinear mirror image method for nonlinear Schrödinger equation: Absorption/emission of one soliton by a boundary, Double and triple-pole solutions for the third-order flow equation of the Kaup-Newell system with zero/nonzero boundary conditions, Large‐time asymptotics to the focusing nonlocal modified Kortweg‐de Vries equation with step‐like boundary conditions, Soliton resolution and large time behavior of solutions to the Cauchy problem for the Novikov equation with a nonzero background, On convergence of form factor expansions in the infinite volume quantum sinh-Gordon model in \(1+1\) dimensions, Long-time asymptotics of solution to the coupled Hirota system with \(4 \times 4\) Lax pair, Three-Wave Interaction Equations: Classical and Nonlocal, A class of third order quasilinear partial differential equations describing spherical or pseudospherical surfaces, Inverse scattering transform and dynamics of soliton solutions for nonlocal focusing modified Korteweg-de Vries equation, Elliptic finite-band potentials of a non-self-adjoint Dirac operator, On the Maxwell‐Bloch system in the sharp‐line limit without solitons, Long-time asymptotics for the coupled complex short-pulse equation with decaying initial data, On asymptotic stability of multi-solitons for the focusing modified Korteweg-de Vries equation, Long‐time asymptotics to the defocusing generalized nonlinear Schrödinger equation with the decaying initial value problem, Bootstrap approach to \(1+1\)-dimensional integrable quantum field theories: the case of the sinh-Gordon model, An inverse scattering formalism for higher-order differential operators, Second order evolution equations which describe pseudospherical surfaces, Completion problems and scattering problems for Dirac type differential equations with singularities, Similarities in a fifth-order evolution equation with and with no singular kernel, Solutions of some class of nonlinear PDEs in mathematical physics, New double periodic and multiple soliton solutions of the generalized \((2 + 1)\)-dimensional Boussinesq equation, Construction of new soliton-like solutions of the (2 + 1) dimensional dispersive long wave equation, Inverse scattering on the half-line for ZS-AKNS systems with integrable potentials, On the asymptotic stability of \(N\)-soliton solutions of the defocusing nonlinear Schrödinger equation, Multidimensional nonlinear evolution equations and inverse scattering, The Riemann boundary value problem on closed Riemann surfaces and integrable systems, Integrable systems and isomonodromy deformations, Long-time asymptotics for the generalized Sasa-Satsuma equation, The D-bar approach to inverse scattering and nonlinear evolutions, Discrete scattering theory, Riemann-Hilbert approach and long-time asymptotics for the three-component derivative nonlinear Schrödinger equation, A Riemann-Hilbert approach for the Novikov equation, Global well-posedness for the derivative nonlinear Schrödinger equation, Local isometric immersions of pseudospherical surfaces described by evolution equations in conservation law form, Long-time asymptotics for the modified complex short pulse equation, Gauge theory of Bäcklund transformations. II, Poisson commuting energies for a system of infinitely many bosons, Riemann-Hilbert approach and long-time asymptotics of the positive flow short-pulse equation, The short pulse equation by a Riemann-Hilbert approach, Long-time asymptotic for the derivative nonlinear Schrödinger equation with step-like initial value, Long-time asymptotic behavior for the discrete defocusing mKdV equation, Constructing of new exact solutions to the GKdV-mKdV equation with any-order nonlinear terms by \((\frac{G'}{G})\)-expansion method, The largest real eigenvalue in the real Ginibre ensemble and its relation to the Zakharov-Shabat system, Solutions to the nonlinear Schrödinger equation with sequences of initial data converging to a Dirac mass, Two-dimensional Toda field equations related to the exceptional algebra \(\mathfrak g_2\): spectral properties of the Lax operators, Long-time asymptotics of a three-component coupled nonlinear Schrödinger system, Long-time asymptotic for the Hirota equation via nonlinear steepest descent method, Initial value problems for integrable systems on a semi-strip, Inverse scattering transform and soliton solutions for square matrix nonlinear Schrödinger equations with non-zero boundary conditions, Linear integral equations and multicomponent nonlinear integrable systems. I, Darboux transformation for the non-isospectral AKNS hierarchy and its asymptotic property, Initial-boundary value problems for integrable evolution equations with \(3\times 3\) Lax pairs, Numerical inverse scattering for the Korteweg-de Vries and modified Korteweg-de Vries equations, Global existence for the derivative nonlinear Schrödinger equation with arbitrary spectral singularities, Factorization of the scattering matrix and the location of the eigenvalues of the Manakov-Zakharov-Shabat system, A series of travelling wave solutions for two variant Boussinesq equations in shallow water waves, Riemann-Hilbert approach for a coherently-coupled nonlinear Schrödinger system associated with a \(4\times 4\) matrix spectral problem, Nonlocal reductions of the multicomponent nonlinear Schrödinger equation on symmetric spaces, On Weyl-type solutions of differential systems with a singularity. The case of discontinuous potential, Sine-Gordon theory in a semi-strip, Adjoint symmetry constraints of the vector KN equations and their integrable coupling system, Boundary value problems for the \(N\)-wave interaction equations, The semiclassical modified nonlinear Schrödinger equation I: Modulation theory and spectral analysis, An operator van der Corput estimate arising from oscillatory Riemann-Hilbert problems, Numerical inverse scattering for the sine-Gordon equation, Exponentially small asymptotics of solutions to the defocusing nonlinear Schrödinger equation, Optimized direct Padé and HPM for solving equation of oxygen diffusion in a spherical cell, A series of new exact solutions for a complex coupled KdV system, Higher order asymptotics for the Hirota equation via Deift-Zhou higher order theory, The nonlinear steepest descent approach for long time behavior of the two-component coupled Sasa-Satsuma equation with a \(5 \times 5\) Lax pair, Soliton resolution for the focusing modified KdV equation, Some special solutions of a generalized Davey-Stewartson system, The nonlinear steepest descent method to long-time asymptotics of the coupled nonlinear Schrödinger equation, Long time asymptotic behavior of the focusing nonlinear Schrödinger equation, Matrix Riemann-Hilbert problems with jumps across Carleson contours, Shallow water wave models with and without singular kernel: existence, uniqueness, and similarities, Conservatory of Kaup-Kupershmidt equation to the concept of fractional derivative with and without singular kernel, Long-time asymptotics of solutions for the coupled dispersive AB system with initial value problems, On the generation of dispersive shock waves, Construction of new soliton-like solutions for the \((2+1)\) dimensional Kadomtsev-Petviashvili equation, Semiclassical soliton ensembles for the three-wave resonant interaction equations, An algebraic method exactly solving two high-dimensional nonlinear evolution equations, Constructing of exact solutions to the KdV and Burgers equations with power-law nonlinearity by the extended \((\frac{G'}{G})\)-expansion method, Algebras of Toeplitz operators with oscillating symbols, A rational generalization of Fan's method and its application to generalized shallow water wave equations, Introduction to magnetic resonance imaging for mathematicians., An extended simplest equation method and its application to several forms of the fifth-order KdV equation, The Deift-Zhou steepest descent method to long-time asymptotics for the Sasa-Satsuma equation, The three-wave equation on the half-line, Large deviations of energy transfers in nonequilibrium CFT and asymptotics of non-local Riemann-Hilbert problems, Spectral analysis and long-time asymptotics for the potential Wadati-Konno-Ichikawa equation, The three-component defocusing nonlinear Schrödinger equation with nonzero boundary conditions, Rational solutions of the Painlevé-III equation: large parameter asymptotics, The Cauchy problem of the Ward equation, Fourth order evolution equations which describe pseudospherical surfaces, Determination of the rich structural wave dynamic solutions to the Caudrey-Dodd-Gibbon equation and the Lax equation, Long-time asymptotics for the defocusing integrable discrete nonlinear Schrödinger equation, Riemann-Hilbert approach to a generalized sine kernel, Riemann-Hilbert theory without local parametrix problems: applications to orthogonal polynomials, A class of quasilinear second order partial differential equations which describe spherical or pseudospherical surfaces, Pseudo-canonical systems with rational Weyl functions: Explicit formulas and applications, A \(\bar{\partial}\)-steepest descent method for oscillatory Riemann-Hilbert problems, Riemann-Hilbert problem and dynamics of soliton solutions of the fifth-order nonlinear Schrödinger equation, Large-order asymptotics for multiple-pole solitons of the focusing nonlinear Schrödinger equation, Spectral analysis and long-time asymptotics of a coupled nonlinear Schrödinger system, Long time asymptotics for the nonlocal mKdV equation with finite density initial data, Application of the nonlinear steepest descent method to the general coupled nonlinear Schrödinger system, On recovering differential systems on a finite interval from spectra, Long-time asymptotics for the Fokas-Lenells equation with decaying initial value problem: without solitons, Long-time asymptotic behavior for the derivative Schrödinger equation with finite density type initial data, Spectral analysis and long-time asymptotics for the coherently-coupled nonlinear Schrödinger system, Multidimensional inverse-scattering and Clifford analysis, On the application of GMRES to oscillatory singular integral equations, Riemann-Hilbert approach to the modified nonlinear Schrödinger equation with non-vanishing asymptotic boundary conditions, Riemann-Hilbert factorizations and inverse scattering for the AKNS- equation with \(L^ 1\)-potentials. I



Cites Work