• Corpus ID: 117886548

# On a proposition relative to linear equations

@article{Darboux1999OnAP,
title={On a proposition relative to linear equations},
author={Gaston Darboux},
journal={arXiv: History and Philosophy of Physics},
year={1999}
}
• G. Darboux
• Published 3 August 1999
• Mathematics
• arXiv: History and Philosophy of Physics
The short Comptes Rendus Note of Darboux, first published in 1882, and also included in his course “Théorie des Surfaces”, second volume, page 210 (1889), was not recognized as important for about one century. In his famous textbook of 1926, Ince mentioned particular cases of Darboux’s result as exercises. However, Ince’s formulation is very close to the framework of supersymmetric quantum mechanics, and therefore should be considered as a valuable contribution. In 1979, V.B. Matveev realized…
38 Citations

### Darboux transformations of supersymmetric Heisenberg magnet model

TheDarboux transformation of supersymmetricHeisenbergmagnetmodel is investigated.We calculate the exact superfieldmultisoliton solutions of theHMmodel by iteration ofDarboux transformation. Explicit

### Stability and Well-posedness in Integrable Nonlinear Evolution Equations

This dissertation is concerned with analysis of orbital stability of solitary waves and well-posedness of the Cauchy problem in the integrable evolution equations. The analysis is developed by using

### Stationary states in a potential well

• Physics
• 2007
We review here in a historical context the topic of stationary states in the quantum world, including the generalization to the primary ideas. We also discuss the stationary states in one dimensional

### BINARY DARBOUX TRANSFORMATION AND QUASIDETERMINANT SOLUTIONS OF THE CHIRAL FIELD

• Mathematics
• 2011
The standard binary Darboux transformation is composed and is used to obtain exact multisoliton solutions of the chiral field model in two dimensions. The solutions are expressed in terms of

### Time-dependent Darboux (supersymmetric) transformations for non-Hermitian quantum systems

• Physics, Mathematics
Journal of Physics A: Mathematical and Theoretical
• 2019
We propose time-dependent Darboux (supersymmetric) transformations that provide a scheme for the calculation of explicitly time-dependent solvable non-Hermitian partner Hamiltonians. Together with

### Quasideterminant solutions of an integrable chiral model in two dimensions

• Mathematics
• 2009
The Darboux transformation is used to obtain multisoliton solutions of the chiral model in two dimensions. The matrix solutions of the principal chiral model and its Lax pair are expressed in terms

### Regularized degenerate multi-solitons

• Mathematics
• 2016
A bstractWe report complex PT$$\mathcal{P}\mathcal{T}$$-symmetric multi-soliton solutions to the Korteweg de-Vries equation that asymptotically contain one-soliton solutions, with each of them

### Nonlocal gauge equivalence: Hirota versus extended continuous Heisenberg and Landau–Lifschitz equation

• Mathematics, Physics
Journal of Physics A: Mathematical and Theoretical
• 2020
We exploit the gauge equivalence between the Hirota equation and the extended continuous Heisenberg equation to investigate how nonlocality properties of one system are inherited by the other. We

### Darboux covariance: A hidden symmetry of perturbed Schwarzschild black holes

• Physics
Physical Review D
• 2021
Starting from the infinite set of possible master equations for the perturbations of Schwarzschild black holes, with master functions linear in the metric perturbations and their first-order