scholarly journals Constraint and Nonlinearization of Supersymmetric Equations with Some Special Forms of Lax Pairs

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Hongmin Li
Keyword(s):  
Special Form ◽  
Evolution Equations ◽  
Lax Pairs ◽  
Boundary Problems ◽  
Classical Evolution

We study the null boundary problems of some classical evolution equations constrained by some special forms of Lax pairs. Furthermore, we present the constraint and nonlinearization of some supersymmetric (SUSY) equations with a special form of Lax pairs and solve the null boundary problems of these SUSY equations under the corresponding constraints.

Feedback theory to the well-posedness of evolution equations

2020 ◽  
Vol 378 (2185) ◽  
pp. 20190616
Author(s):  
S. Boulite ◽  
S. Hadd ◽  
L. Maniar
Keyword(s):  
Evolution Equations ◽  
Semigroup Theory ◽  
Well Posedness ◽  
Boundary Problems ◽  
Neutral Equations ◽  
Infinite Dimensional ◽  
Research Activities ◽  
Semigroup Approach ◽  
History Of ◽  
And Control

In this paper, we cross the boundary between semigroup theory and general infinite-dimensional systems to bridge the isolated research activities in the two areas. Indeed, we first give a chronological history of the development of the semigroup approach for control theory. Second, we use the feedback theory to prove the well-posedness of a class of dynamic boundary problems. Third, the obtained results are applied to the well-posedness of neutral equations with non-autonomous past. We will also see that the strong connection between semigroup and control theories lies in feedback theory, where different kinds of perturbations appear. This article is part of the theme issue ‘Semigroup applications everywhere’.

The Bargmann Constraint and Integrable System for a Second-Order Spectral Problem

2015 ◽  
Vol 70 (11) ◽  
pp. 913-917
Author(s):  
Wei Liu ◽  
Yafeng Liu ◽  
Shujuan Yuan
Keyword(s):  
Coordinate System ◽  
Spectral Problem ◽  
Integrable System ◽  
Evolution Equations ◽  
Lagrange Equations ◽  
Lax Pairs ◽  
Infinite Dimensional ◽  
Hamilton System ◽  
Finite Dimensional ◽  
Dimensional Soliton

AbstractIn this article, the Bargmann system related to the spectral problem (∂2+q∂+∂q+r)φ=λφ+λφx is discussed. By the Euler–Lagrange equations and the Legendre transformations, a suitable Jacobi–Ostrogradsky coordinate system is obtained. So the Lax pairs of the aforementioned spectral problem are nonlinearised. A new kind of finite-dimensional Hamilton system is generated. Moreover, the involutive solutions of the evolution equations for the infinite-dimensional soliton system are derived.

Maximum entropy principle and classical evolution equations with source terms

2007 ◽  
Vol 374 (2) ◽  
pp. 573-584 ◽  
Author(s):  
J-H. Schönfeldt ◽  
N. Jimenez ◽  
A.R. Plastino ◽  
A. Plastino ◽  
M. Casas
Keyword(s):  
Maximum Entropy ◽  
Evolution Equations ◽  
Maximum Entropy Principle ◽  
Source Terms ◽  
Entropy Principle ◽  
Classical Evolution

scholarly journals Multicomponent Nonlinear Evolution Equations of the Heisenberg Ferromagnet Type: Local Versus Nonlocal Reductions

2021 ◽  
pp. 274-285
Author(s):  
Tihomir Valchev
Keyword(s):  
Heisenberg Model ◽  
Symmetric Spaces ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Heisenberg Ferromagnet ◽  
Lax Pairs ◽  
Hermitian Symmetric Spaces ◽  
Integrable Deformation

This work is dedicated to systems of matrix nonlinear evolution equations related to Hermitian symmetric spaces of the type $\mathbf{A.III}$. The systems under consideration generalize the $1+1$ dimensional Heisenberg ferromagnet equation in the sense that their Lax pairs are linear bundles in pole gauge like for the original Heisenberg model. Here we present certain local and nonlocal reductions. A local integrable deformation and some of its reductions are discussed as well.

A New Hierarchy of Evolution Equations and its Integrable System

2010 ◽  
Vol 143-144 ◽  
pp. 1200-1203
Author(s):  
Shu Juan Yuan ◽  
Mei Xia Chen
Keyword(s):  
Eigenvalue Problem ◽  
Integrable System ◽  
Evolution Equations ◽  
Second Order ◽  
Matrix Eigenvalue Problem ◽  
Lax Pairs ◽  
Matrix Eigenvalue ◽  
Hamilton System ◽  
Finite Dimensional ◽  
Order Matrix

The second-order matrix eigenvalue problem is discussed by means of the nonlinearization of the Lax pairs,then based on the Bargmann constraint between the potential and the eigenfunctions,a new finite-dimensional Hamilton system is abtained by nonlinearization of the eigenvalue problem and the involutive solutions of the evolution equations are abtained

scholarly journals Scaling invariant Lax pairs of nonlinear evolution equations

2012 ◽  
Vol 91 (2) ◽  
pp. 381-402 ◽  
Author(s):  
Mark Hickman ◽  
Willy Hereman ◽  
Jennifer Larue ◽  
Ünal Göktaş
Keyword(s):  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Lax Pairs ◽  
Scaling Invariant
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