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IST Versus PDE: A Comparative Study (Q2787294)

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Language	Label	Description	Also known as
English	IST Versus PDE: A Comparative Study	scientific article

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scholarly article

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IST Versus PDE: A Comparative Study (English)

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Christian Klein

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Jean Claude Saut

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Hamiltonian Partial Differential Equations and Applications

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publication date

25 February 2016

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full work available at URL

https://arxiv.org/abs/1409.2020

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MaRDI profile type

MaRDI publication profile

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Nonlocal models for nonlinear, dispersive waves

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The Inverse Scattering Transform for the Benjamin‐Ono Equation—A Pivot to Multidimensional Problems

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On the evolution of packets of water waves

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The Cauchy Problem for the Kadomtsev–Petviashili II Equation with Nondecaying Data along a Line

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On the initial value problem for the KPII equation with data that do not decay along a line

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Total Positivity and the Stability of Internal Waves in Stratified Fluids of Finite Depth

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On the exact solutions of the intermediate long-wave equation

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Sufficient conditions for stability of solitary-wave solutions of model equations for long waves

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On the stability of KdV multi-solitons.

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Uniqueness and related analytic properties for the Benjamin-Ono equation -- A nonlinear Neumann problem in the plane

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The Benjamin-Ono equation recursivity of linearization maps - Lax pairs

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Inverse scattering transform method and soliton solutions for Davey- Stewartson II equation

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Scattering and inverse scattering for first order systems

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On the stability of certain spin models in \(2+1\) dimensions

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Uniform decay estimates for a class of oscillatory integrals and applications

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Dispersion Estimates for Third Order Equations in Two Dimensions

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Wave Instabilities

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NUMERICAL STUDY OF ELLIPTIC-HYPERBOLIC DAVEY–STEWARTSON SYSTEM: DROMIONS SIMULATION AND BLOW-UP

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On the linear wave regime of the Gross-Pitaevskii equation

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On the Korteweg–de Vries Long-Wave Approximation of the Gross–Pitaevskii Equation II

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On the KPI transonic limit of two-dimensional Gross-Pitaevskii travelling waves

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Orbital stability of the black soliton for the Gross-Pitaevskii equation

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On the stability theory of solitary waves

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Boussinesq equations and other systems for small-amplitude long waves in nonlinear dispersive media. I: Derivation and linear theory

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Asymptotic models for internal waves

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On the stability of solitary-wave solutions of model equations for long waves

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Solitary waves of generalized Kadomtsev-Petviashvili equations

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Symmetries and Decay of the Generalized Kadomtsev--Petviashvili Solitary Waves

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Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation

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On the Cauchy problem for the Kadomtsev-Petviashvili equation

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Properties of the Benjamin–Ono equation

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The <i>N</i> -soliton solution of the Benjamin-Ono equation

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Orbital stability of standing waves for some nonlinear Schrödinger equations

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The KdV/KP-I Limit of the Nonlinear Schrödinger Equation

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On the existence of standing waves for a davey–stewartson system

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The scattering transform for the Benjamin-Ono equation

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Justification of and long-wave correction to Davey-Stewartson systems from quadratic hyperbolic systems

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An existence theory for water waves and the boussinesq and korteweg-devries scaling limits

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On three-dimensional packets of surface waves

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An extension of the steepest descent method for Riemann-Hilbert problems: The small dispersion limit of the Korteweg-de Vries (KdV) equation

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A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation

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Long-time asymptotics for integrable systems. Higher order theory

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Long‐time asymptotics for solutions of the NLS equation with initial data in a weighted Sobolev space

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The black solitons of one-dimensional NLS equations

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On two-dimensional packets of capillary-gravity waves

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On the Inverse Scattering of the Time-Dependent Schrödinger Equation and the Associated Kadomtsev-Petviashvili (I) Equation

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Inverse scattering transform for the KPI equation on the background of a one-line soliton*

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Interaction of lumps with a line soliton for the DSII equation

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Dromions and a boundary value problem for the Davey-Stewartson 1 equation

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The Cauchy problem for the Kadomtsev–Petviashvili–I equation without the zero mass constraint

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On the solvability of the N-wave, Davey-Stewartson and Kadomtsev-Petviashvili equations

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The Cauchy Problem for Defocusing Nonlinear Schrödinger Equations with Non-Vanishing Initial Data at Infinity

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The Cauchy problem for the Gross--Pitaevskii equation

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Orbital stability of traveling waves for the one-dimensional Gross-Pitaevskii equation

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On the initial value problem for the Davey-Stewartson systems

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Nonexistence of travelling wave solutions to nonelliptic nonlinear Schrödinger equations

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Nonelliptic Schrödinger equations

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Asymptotics of the solitary waves for the generalized Kadomtsev-Petviashvili equations

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Nonsingularity of the direct scattering transform for the KP II equation with a real exponentially decaying-at-infinity potential

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Scattering transformation at fixed non-zero energy for the two-dimensional Schrödinger operator with potential decaying at infinity

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Rational solitons of the Veselov-Novikov equations are reflectionless two-dimensional potentials at fixed energy

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Two-dimensional ``inverse scattering problem'' for negative energies and generalized-analytic functions. I: Energies below the ground state

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Well-posedness for the Kadomtsev-Petviashvili II equation and generalisations

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Erratum to ``Well-posedness and scattering for the KP-II equation in a critical space'' [Ann. I. H. Poincaré - AN 26 (3) (2009) 917-941]

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Local existence in time of solutions to the elliptic-hyperbolic Davey-Stewartson system without smallness condition on the data

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Local existence in time of small solutions to the elliptic-hyperbolic Davey-Stewartson system in the usual Sobolev space

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Global existence and asymptotic behaviour in time of small solutions to the elliptic - hyperbolic Davey - Stewartson system

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Asymptotics for large time of global solutions to the generalized Kadomtsev-Petviashvili equation

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LOCAL AND GLOBAL CAUCHY PROBLEMS FOR THE KADOMTSEV–PETVIASHVILI (KP–II) EQUATION IN SOBOLEV SPACES OF NEGATIVE INDICES

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Global well-posedness of the Benjamin–Ono equation in low-regularity spaces

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Global well-posedness of the KP-I initial-value problem in the energy space

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On the cauchy problem for the benjamin-ono equation

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On equations of KP-type

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Multi-Vortex Solutions of a Two-Dimensional Nonlinear Wave Equation

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Lagrange multiplier formalism for a spin-3/2 field

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Multi-soliton solutions in a finite depth fluid

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Long wave asymptotics. Integrable equations as asymptotic limits of non-linear systems

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A large-time asymptotics for the solution of the Cauchy problem for the Novikov–Veselov equation at negative energy with non-singular scattering data

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Large time asymptotics for the Grinevich-Zakharov potentials

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Absence of exponentially localized solitons for the Novikov–Veselov equation at negative energy

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On the local and global well-posedness theory for the KP-I equation

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Asymptotic stability of solitons for the Benjamin-Ono equation

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Global well-posedness in the energy space for a modified KP II equation via the Miura transform

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The Cauchy problem for the hyperbolic–elliptic Ishimori system and Schrödinger maps

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Well-Posedness of the Initial Value Problem for the Korteweg-de Vries Equation

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Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle

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Radial standing and self-similar waves for the hyperbolic cubic NLS in 2D

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Dromion Perturbation for the Davey-Stewartson-1 Equations

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Numerical study of shock formation in the dispersionless Kadomtsev-Petviashvili equation and dispersive regularizations

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Numerical study of the semiclassical limit of the Davey–Stewartson II equations

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Numerical study of blow up and stability of solutions of generalized Kadomtsev-Petviashvili equations

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A numerical approach to blow-up issues for dispersive perturbations of Burgers' equation

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A numerical approach to Blow-up issues for Davey-Stewartson II systems

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Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation

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Numerical study of blow-up in the Davey-Stewartson system

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Local Smoothing and Local Solvability for Third Order Dispersive Equations

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On finite energy solutions of the KP-I equation

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Direct and inverse scattering problems of the nonlinear intermediate long wave equation

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Inverse Spectral Transform for the Nonlinear Evolution Equation Generating the Davey-Stewartson and Ishimori Equations

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Integrable Equations in Nonlinear Geometrical Optics

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Weakly transverse Boussinesq systems and the Kadomtsev–Petviashvili approximation

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Integrals of nonlinear equations of evolution and solitary waves

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Generalized internal long waves equations: Construction, Hamiltonian structure, and conservation laws

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Electromagnetic waves in ferromagnets: a Davey-Stewartson-type model

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Stability and instability of traveling solitonic bubbles.

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On the Davey-Stewartson systems

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Dispersive Perturbations of Burgers and Hyperbolic Equations I: Local Theory

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Blow up and instability of solitary-wave solutions to a generalized Kadomtsev-Petviashvili equation

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The inverse scattering transform for the time-dependent Schrödinger equation and Kadomtsev-Petviashvili equation

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Asymptotic stability of solitons of the subcritical gKdV equations revisited

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Asymptotic stability of solitons of the gKdV equations with general nonlinearity

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Inelastic interaction of nearly equal solitons for the BBM equation

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Description of the inelastic collision of two solitary waves for the BBM equation

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Exact multi-soliton solution of the Benjamin-Ono equation

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Interaction of the Benjamin-Ono solitons

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Bilinear transformation method

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Localised coherent solutions of the DSI and DSII equations -- a numerical study

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Global Well-Posedness and Limit Behavior for a Higher-Order Benjamin-Ono Equation

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Ill-Posedness Issues for the Benjamin--Ono and Related Equations

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Well-posedness and ill-posedness results for the Kadomtsev-Petviashvili-I equation

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Remarks on the Mass Constraint for KP-Type Equations

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Global well-posedness for the KP-I equation on the background of a non-localized solution

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Global well-posedness for the KP-II equation on the background of a non-localized solution

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Orbital stability of double solitons for the Benjamin-Ono equation

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Stability and instability of standing waves for the generalized Davey- Stewartson system

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Exact blow-up solutions to the Cauchy problem for the Davey–Stewartson systems

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The focusing singularity of the Davey-Stewartson equations for gravity- capillary surface waves

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Rational solutions of the Kadomtsev–Petviashvili hierarchy and the dynamics of their poles. I. New form of a general rational solution

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Eigenfunctions and eigenvalues for a scalar Riemann-Hilbert problem associated to inverse scattering

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Spectral decomposition for the Dirac system associated to the DSII equation

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Similarity Solutions of Some Two-Space-Dimensional Nonlinear Wave Evolution Equations

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Transverse nonlinear instability of solitary waves for some Hamiltonian PDE's

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Transverse nonlinear instability for two-dimensional dispersive models

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A simple criterion of transverse linear instability for solitary waves

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<i>N</i>-Soliton Solution of the Two-Dimensional Korteweg-deVries Equation

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Two-dimensional lumps in nonlinear dispersive systems

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The Cauchy problem for higher-order KP equations

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The Cauchy problem for the fifth order KP equations

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An application of the inverse scattering transform to the modified intermediate long wave equation

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Who cares about integrability?

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The Cauchy problem for the Ishimori equations

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An inverse scattering transform for the Davey-Stewartson II equations. I

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An inverse scattering transform for the Davey-Stewartson II equations. II

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An inverse scattering transform for the Davey-Stewartson II equations. III

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Long-time decay of the solutions of the Davey-Stewartson II equations

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The Cauchy problem for the Ishimori equation

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Square integrability and uniqueness of the solutions of the Kadomtsev-Petviashvili-I equation

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GLOBAL WELL-POSEDNESS OF THE BENJAMIN–ONO EQUATION IN H<sup>1</sup>(<b>R</b>)

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Why are solitons stable?

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On the discrete spectrum of the nonstationary Schrödinger equation and multipole lumps of the Kadomtsev-Petviashvili I equation

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Inverse scattering for the heat operator and evolutions in \(2+1\) variables

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Multi-scale expansions in the theory of systems integrable by the inverse scattering transform

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Inverse scattering transform for the time dependent Schrödinger equation with applications to the KPI equation

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Identifiers

zbMATH Open document ID

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10.1007/978-1-4939-2950-4_14

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:2787294

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