# Hamiltonian methods in the theory of solitons

@inproceedings{Faddeev1987HamiltonianMI, title={Hamiltonian methods in the theory of solitons}, author={Ludwig D. Faddeev and Leon A. Takhtajan}, year={1987} }

The Nonlinear Schrodinger Equation (NS Model).- Zero Curvature Representation.- The Riemann Problem.- The Hamiltonian Formulation.- General Theory of Integrable Evolution Equations.- Basic Examples and Their General Properties.- Fundamental Continuous Models.- Fundamental Models on the Lattice.- Lie-Algebraic Approach to the Classification and Analysis of Integrable Models.- Conclusion.- Conclusion.

## 2,251 Citations

The Hamiltonian dynamics of the soliton of the discrete nonlinear Schrödinger equation

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- 2001

Hamiltonian equations are formulated in terms of collective variables describing the dynamics of the soliton of an integrable nonlinear Schrödinger equation on a 1D lattice. Earlier, similar…

On Separation of Variables for Integrable Equations of Soliton Type

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- 2007

Abstract We propose a general scheme for separation of variables in the integrable Hamiltonian systems on orbits of the loop algebra (2, C) x P(λ, λ–1). In particular, we illustrate the scheme by…

Nonlocal integrals and conservation laws in the theory of nonlinear solitons

- Mathematics
- 2008

It is natural to investigate properties of solutions to nonstationary linear equations of mathematical physics by means of time-invariant spaces of linear functionals. In the framework of this…

The matrix nonlinear Schrödinger equation in dimension 2

- Mathematics
- 2001

In this paper we study the existence of global solutions to the Cauchy problem for the matrix nonlinear Schrodinger equation (MNLS) in 2 space dimensions. A sharp condition for the global existence…

BI-HAMILTONIAN STRUCTURE OF THE SUPERSYMMETRIC NONLINEAR SCHRÖDINGER EQUATION

- Physics
- 1995

We show that the supersymmetric nonlinear Schrodinger equation is a bi-Hamiltonian integrable system. We obtain the two Hamiltonian structures of the theory from the ones of the supersymmetric…

N-soliton solutions and perturbation theory for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions

- Mathematics, Physics
- 2007

We present a simple approach for finding an N-soliton solution and the corresponding Jost solutions of the derivative nonlinear Schrodinger equation with nonvanishing boundary conditions. Soliton…

Holomorphic solutions of soliton equations

- MathematicsTransactions of the Moscow Mathematical Society
- 2022

We present a holomorphic version of the inverse scattering method for soliton equations of parabolic type in two-dimensional space-time. It enables one to construct examples of solutions holomorphic…

Soliton Solution of the Integrable Coupled Nonlinear Schrodinger Equation of Manakov Type

- Physics, Mathematics
- 1998

The soliton solution of the integrable coupled nonlinear Schrodinger equa- tion (NLS) of Manakov typeisinvestigated by using Zakharov-Shabat (ZS) scheme. We get the bright N-solitons solution by…

Conformal Algebras and Non-Linear Differential Equations

- Mathematics
- 1990

The method of Hamiltonian reduction used by Drinfeld and Sokolov in the theory of integrable non-linear differential equations, is applied to two dimensional field theories. We show that conformai…

Leading-order temporal asymptotics of the modified nonlinear Schrödinger equation: solitonless sector

- Mathematics
- 1997

Using the matrix Riemann - Hilbert factorization approach for nonlinear evolution equations (NLEEs) integrable in the sense of the inverse scattering method, we obtain, in the solitonless sector, the…