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Direct and inverse scattering transforms with arbitrary spectral singularities

https://doi.org/10.1002/cpa.3160420702
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Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1002/cpa.3160370105openalex-snapshot
Scattering and inverse scattering for first order systems
inferredcites →https://doi.org/10.1002/cpa.3160380103openalex-snapshot
Inverse scattering and evolution equations
inferredcites →https://doi.org/10.1002/sapm1974534249openalex-snapshot
The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
inferredcites →https://doi.org/10.1002/sapm1986743177openalex-snapshot
On the Solution of the Generalized Wave and Generalized Sine‐Gordon Equations
inferredcites →https://doi.org/10.1007/978-3-0348-6266-0openalex-snapshot
Factorization of Measurable Matrix Functions
inferredcites →https://doi.org/10.1007/bf01077483openalex-snapshot
Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II
inferredcites →https://doi.org/10.1016/0167-2789(82)90004-5openalex-snapshot
The inverse problem for a general N × N spectral equation
inferredcites →https://doi.org/10.1016/0375-9601(77)90727-7openalex-snapshot
Integration of the continuous Heisenberg spin chain through the inverse scattering method
inferredcites →https://doi.org/10.1088/0266-5611/3/4/009openalex-snapshot
Scattering and inverse scattering for first-order systems: II
inferredcites →https://doi.org/10.1090/surv/028openalex-snapshot
Direct and Inverse Scattering on the Line
inferredcites →https://doi.org/10.1137/0520065openalex-snapshot
The Riemann–Hilbert Problem and Inverse Scattering
inferredcites →https://doi.org/10.1137/0521039openalex-snapshot
Flat Connections and Scattering Theory on the Line

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Incoming claims: where this work appears in other papers’ reference lists and arguments.

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On Matrix-Valued Herglotz Functions
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A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation
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Direct and inverse scattering on the line with arbitrary singularities
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Uniqueness results for skew‐self‐adjoint Dirac system with rectangular potential
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The Inverse Scattering Transform on the Line
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Solvability of the derivative nonlinear Schrödinger equation and the massive thirring model
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Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation
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The Three-Component Defocusing Nonlinear Schrödinger Equation with Nonzero Boundary Conditions
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Semiclassical Soliton Ensembles for the Three-Wave Resonant Interaction Equations
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Soliton Resolution for the Derivative Nonlinear Schrödinger Equation
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The Derivative Nonlinear Schrödinger Equation with Zero/Nonzero Boundary Conditions: Inverse Scattering Transforms and N-Double-Pole Solutions
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Asymptotics of Recurrence Relation Coefficients, Hankel Determinant Ratios, and Root Products Associated with Laurent Polynomials Orthogonal with Respect to Varying Exponential Weights
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Rational Functions with a General Distribution of Poles on the Real Line Orthogonal with Respect to Varying Exponential Weights: I
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Riemann–Hilbert approach and N double-pole solutions for the third-order flow equation of nonlinear derivative Schrödinger-type equation
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Riemann–Hilbert approaches of an M-coupled nonlinear Schrödinger system with variable coefficients and the associated nonlocal equation
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Long Time Asymptotics Behavior of the Focusing Nonlinear Kundu-Eckhaus Equation
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On Behavior Analysis of Solutions for the Modified Complex Short Pulse Equation in the Space-Time Soliton Regions
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Semigroup estimates and stability/instability results for the linearized three waves interaction equations
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The Riemann-Hilbert approach for the focusing Hirota equation with single and double poles
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Inverse Scattering Transform for Nonlinear Schrödinger Systems on a Nontrivial Background: A Survey of Classical Results, New Developments and Future Directions
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Integrability and a new breed of solitons of an NLS type equation in 2+1 dimensions
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Zakharov-Shabat Inverse Scattering
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Poisson commuting energies for a system of infinitely many bosons
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On the soliton resolution and the asymptotic stability of N-soliton solution for the Wadati-Konno-Ichikawa equation with finite density initial data in space-time solitonic regions
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Inverse scattering transformation for generalized nonlinear Schrödinger equation
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Long time asymptotic behavior of the focusing nonlinear Schrödinger equation
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New integrable multi-Lévy-index and mixed fractional nonlinear soliton hierarchies
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Focusing and defocusing Hirota equations with non-zero boundary conditions: Inverse scattering transforms and soliton solutions
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Riemann-Hilbert Approach for a Higher-Order Chen-Lee-Liu Equation with High-Order Poles
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Soliton resolution for the generalized complex short pulse equation with the weighted Sobolev initial data
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Soliton resolution for the complex short pulse equation with weighted Sobolev initial data in space-time solitonic regions
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Soliton resolution for the complex short-pulse positive flow with weighted Sobolev initial data in the space-time soliton regions
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L2-Sobolev space bijectivity and existence of global solutions for the matrix nonlinear Schrödinger equations
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Soliton resolution and long-time asymptotics for the Camassa-Holm positive flow with the presence of discrete spectra
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The Cauchy problem of an integrable complex nonlinear model with weighted Sobolev initial data: soliton resolution and asymptotic stability of N-solitons
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Riemann-Hilbert approach for the Kundu equation with non-vanishing boundary conditions: Simple and double poles
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Inverse scattering transform for the coupled Lakshmanan–Porsezian–Daniel equations with non-zero boundary conditions in optical fiber communications
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Adjoint symmetry constraints of the vector KN equations and their integrable coupling system
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Inverse scattering transform for the defocusing nonlinear Schrödinger equation with fully asymmetric non-zero boundary conditions
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Inverse scattering transform and soliton solutions for square matrix nonlinear Schrödinger equations with non-zero boundary conditions
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Inverse scattering transforms and soliton solutions of focusing and defocusing nonlocal mKdV equations with non-zero boundary conditions
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Focusing and defocusing mKdV equations with nonzero boundary conditions: Inverse scattering transforms and soliton interactions
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Asymptotic analysis of high-order solitons for the Hirota equation
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Asymptotic stage of modulation instability for the nonlocal nonlinear Schrödinger equation
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Darboux transformation and solitonic solution to the coupled complex short pulse equation
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Large and infinite-order solitons of the coupled nonlinear Schrödinger equation
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Inverse scattering transform for the defocusing–defocusing coupled Hirota equations with non-zero boundary conditions: Multiple double-pole solutions
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Spectral theory for non-self-adjoint Dirac operators with periodic potentials and inverse scattering transform for the focusing nonlinear Schrödinger equation with periodic boundary conditions
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Long-time asymptotic behavior of the generalized coupled high-order nonlinear Schrödinger equation with solitons
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Long-time asymptotics of the coupled nonlinear Schrödinger equation in a weighted Sobolev space
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Soliton resolution for the generalized WKI equation with the weighted Sobolev initial data in space-time soliton regions
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Inverse scattering and N-triple-pole soliton and breather solutions of the focusing nonlinear Schrödinger hierarchy with nonzero boundary conditions
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Inverse Scattering on the Line—an Overview
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Exponentially small asymptotics of solutions to the defocusing nonlinear Schrödinger equation
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Nonlinear Dispersive Waves
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Matrix spectral problem with multiple-order jumps and poles
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Long-Time Asymptotics of Solutions to the Cauchy Problem for the Defocusing Nonlinear Schrödinger Equation with Finite-Density Initial Data. II. Dark Solitons on Continua
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Reconstruction of Non-Self-Adjoint Differential Systems on the Half-Line from the Weyl Matrix
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Perturbation theory for nearly integrable multicomponent nonlinear PDEs
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General soliton matrices in the Riemann–Hilbert problem for integrable nonlinear equations
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The generalised Zakharov–Shabat system and the gauge group action
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Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions
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Completeness of the eigenfunctions for the Caudrey–Beals–Coifman system
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Focusing nonlinear Schrödinger equation with infinitely many solitons
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Hamiltonian structure for degenerate AKNS systems
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Couple coefficients for the two-block AKNS system
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Asymptotic stability of N -soliton solutions for the modified nonlinear Schrödinger equation
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Strong regularizing effect of integrable systems
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Long-time asymptotics for the pure radiation solution of the sine—gordon equation
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Inverse Scattering Transform and Solitons for Square Matrix Nonlinear Schrödinger Equations with Mixed Sign Reductions and Nonzero Boundary Conditions
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Leading-order temporal asymptotics of the modified nonlinear Schrödinger equation: solitonless sector
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Large-time continuum asymptotics of dark solitons
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Inverse problems for the matrix Sturm–Liouville equation on a finite interval
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Exponentially small asymptotics of solutions to the defocusing nonlinear Schrödinger equation: II
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A new Riemann–Hilbert problem in a model of stimulated Raman Scattering
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L 2 -Sobolev space bijectivity of the inverse scattering of a 3 × 3 AKNS system
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Inverse scattering transforms of the inhomogeneous fifth-order nonlinear Schrödinger equation with zero/nonzero boundary conditions
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Long-time asymptotics of solutions to the Cauchy problem for the defocusing non-linear Schrödinger equation with finite-density initial data. I. Solitonless sector
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Riemann-Hilbert factorization of matrices invariant under inversion in a circle
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The derivative nonlinear Schrödinger equation: Global well-posedness and soliton resolution
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On the focusing non-linear Schrödinger equation with non-zero boundary conditions and double poles
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Nonlinear Waves & Hamiltonian Systems
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Copyright Page
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.002.0004openalex-snapshot
Dedication
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.002.0005openalex-snapshot
Preface
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0001openalex-snapshot
Introduction and Motivation
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0002openalex-snapshot
Linear Dispersive Wave Equations
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0003openalex-snapshot
Nonlinear Dispersive Wave Equations
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0004openalex-snapshot
The Korteweg–de Vries (KdV) Equation
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0005openalex-snapshot
From Boussinesq to KdV – Boussinesq Solitons as KdV Solitons
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0006openalex-snapshot
Traveling Wave Reduction, Elliptic Functions, and Connections to KdV
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0007openalex-snapshot
Burgers and KdV–Burgers Equations – Regularized Shock Waves
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0008openalex-snapshot
A Final Touch From KdV: Invariances and Self-Similar Solutions
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Spectral Methods
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0010openalex-snapshot
Bäcklund Transformation for the KdV
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0011openalex-snapshot
Inverse Scattering Transform I – the KdV Equation*
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0012openalex-snapshot
Direct Perturbation Theory for Solitons*
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The Kadomtsev–Petviashvili Equation*
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Another Class of Models: Nonlinear Klein–Gordon Equations
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0015openalex-snapshot
Additional Tools/Results for Klein–Gordon Equations
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0016openalex-snapshot
Klein–Gordon to NLS Connection – Breathers as NLS Solitons
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0017openalex-snapshot
Interlude: Numerical Considerations for Nonlinear Wave Equations
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0018openalex-snapshot
The Nonlinear Schrödinger (NLS) Equation
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0019openalex-snapshot
NLS to KdV Connection – Dark Solitons as KdV Solitons
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0020openalex-snapshot
Actions, Symmetries, Conservation Laws, Noether’s Theorem, and All That
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0021openalex-snapshot
Applications of Conservation Laws – Adiabatic Perturbation Method
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0022openalex-snapshot
Numerical Techniques for NLS
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0023openalex-snapshot
Inverse Scattering Transform II – the NLS Equation*
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0024openalex-snapshot
The Gross–Pitaevskii (GP) Equation
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0025openalex-snapshot
Variational Approximation for the NLS and GP Equations
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0026openalex-snapshot
Stability Analysis in 1D
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0027openalex-snapshot
Multi-Component Systems
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0028openalex-snapshot
Transverse Instability of Solitons Stripes – Perturbative Approach
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0029openalex-snapshot
Transverse Instability of Dark Stripes – Adiabatic Invariant Approach
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0030openalex-snapshot
Vortices in the 2D Defocusing NLS
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0031openalex-snapshot
The Discrete Klein–Gordon Model
inferred← citeshttps://doi.org/10.1093/oso/9780192843234.003.0032openalex-snapshot
Discrete Models of the Nonlinear Schrödinger Type
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From Toda to FPUT and Beyond
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Interacting domain walls in an easy-plane ferromagnet
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Solitonic model of the condensate
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Quasiradiation solution to the compound integrable model
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On the Capacity of b-Modulated Nonlinear Frequency Division Multiplexing
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Higher‐Order Solitons in the N‐Wave System
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High‐Order Soliton Solution of Landau–Lifshitz Equation
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CBC Systems with Mikhailov Reductions by Coxeter Automorphism: I. Spectral Theory of the Recursion Operators
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Inverse Scattering Transform and Solitons for Square Matrix Nonlinear Schrödinger Equations
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Semiclassical dynamics and coherent soliton condensates in self‐focusing nonlinear media with periodic initial conditions
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Inverse scattering transform for the focusing nonlinear Schrödinger equation with counterpropagating flows
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Inverse scattering transform for the two‐component Gerdjikov–Ivanov equation with nonzero boundary conditions: Dark‐dark solitons
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On the global existence for the modified Camassa–Holm equation
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Uniqueness of lump solution to the KP‐I equation
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Dynamics of a light field in a composite integrable model
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Three-Wave Interaction Equations: Classical and Nonlocal
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Soliton resolution for the modified short pulse equation with the weighted Sobolev initial data
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Asymptotics of Laurent polynomials of even degree orthogonal with respect to varying exponential weights
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An inverse problem for the non-selfadjoint matrix Sturm–Liouville equation on the half-line
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• Expansions Over Adjoint Solutions for the Caudrey-Beals-Coifman System with Reductions of Mikhailov Type
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Recursion Operators and Expansions Over Adjoint Solutions for the Caudrey-Beals-Coifman System with Reductions of Mikhailov Type
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