Factorization of non-linear supersymmetry in one-dimensional Quantum Mechanics. II: proofs of theorems on reducibility [PDF]
, 2008 In this paper, we continue to study factorization of supersymmetric (SUSY) transformations in one-dimensional Quantum Mechanics into chains of elementary Darboux transformations with nonsingular coefficients.
A. A. Andrianov +26 more
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Stochastic LU factorizations, Darboux transformations and urn models [PDF]
Journal of Applied Probability, 2017 We consider upper‒lower (UL) (and lower‒upper (LU)) factorizations of the one-step transition probability matrix of a random walk with the state space of nonnegative integers, with the condition that both upper and lower triangular matrices in the ...
F. Grünbaum, Manuel D. de la Iglesia
semanticscholar +1 more source
Non-polynomial extensions of solvable potentials a la Abraham-Moses [PDF]
, 2013 Abraham-Moses transformations, besides Darboux transformations, are well-known procedures to generate extensions of solvable potentials in one-dimensional quantum mechanics.
Darboux G., Ryu Sasaki, Satoru Odake
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MKdV方程和SG方程的可积曲面的构造(Conformation of soliton surfaces of MKdV equation and SG equation)
Zhejiang Daxue xuebao. Lixue ban, 2010 The soliton solutions and the soliton surfaces of Modified Korteweg-de Vries equation (MKdV) and Sine-Gordon (SG) equation by the n-fold Darboux transformation are given out.
ZHANGLing(张玲), DINGNan(丁楠)
doaj +1 more source
On form-preserving transformations for the time-dependent Schr\"odinger equation [PDF]
, 1999 In this paper we point out a close connection between the Darboux transformation and the group of point transformations which preserve the form of the time-dependent Schr\"odinger equation (TDSE).
Artemio González-López +4 more
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Solitons and the generalized Cole-Hopf substitutions
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2013 This paper examines the relationship between the method of the inverse problem and the method of generalized Cole-Hopf substitutions. The relationship between these methods is established by comparing the method of Darboux transformations and the method ...
V. M. Zhuravlev, A. N. Byzykchi
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Darboux Transformations and Global Explicit Solutions for Nonlocal Davey–Stewartson I Equation [PDF]
, 2016 For the nonlocal Davey–Stewartson I equation, the Darboux transformation is considered and explicit expressions of the solutions are obtained. Like other nonlocal equations, many solutions of this equation may have singularities.
Zixiang Zhou
semanticscholar +1 more source
Darboux transformation and multi-soliton solutions of Two-Boson hierarchy
, 2010 We study Darboux transformations for the two boson (TB) hierarchy both in the scalar as well as in the matrix descriptions of the linear equation. While Darboux transformations have been extensively studied for integrable models based on $SL(2,R)$ within
Ablowitz M. J. +6 more
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Acta et Commentationes: Ştiinţe Exacte şi ale Naturii, 2019 The Lotka-Volterra cubicdifferential systems with (1:-2)-singularity possessing invariant straight lines of two direction and total multiplicity six are classified.
Silvia TURUTA
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On Darboux transformations for the derivative nonlinear Schr\"odinger equation [PDF]
, 2014 We consider Darboux transformations for the derivative nonlinear Schr\"odinger equation. A new theorem for Darboux transformations of operators with no derivative term are presented and proved.
Nimmo, Jonathan J. C., Yilmaz, Halis
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