相关论文: Comment on "Darboux transformation and classificat…
Darboux transformations are non-group type symmetries of linear differential operators. One can define Darboux transformations algebraically by the intertwining relation $ML=L_1M$ or the intertwining relation $ML=L_1N$ in the cases when the…
I would like to thank the authors for their interesting and very clearly presented paper discussing probabilistic solvers for ODEs and PDEs.
We present a generalized study and characterization of the integrability properties of the derivative non-linear Schr\"odinger equation in 1+1 dimensions. A Lax pair is derived for this equation by means of a Miura transformation and the…
This article encloses some results on nonncommutative analogue of nonabelian equations of Langmuir oscillations. One of the main contributions of this work is to construct the Darbboux transformation for the solution of that equation in…
This posting addresses the incorrect information (about my papers) and analysis provided in the following articles: arXiv:1405.4000/Nanotechnology 26, 245202 (2015), arXiv:1412.7765/Scientific Reports 4, 7553 (2014), Appl. Phys. Lett. 105,…
We correct an error in [I. Kangasniemi, and J. Onninen, On the heterogeneous distortion inequality. Math. Ann. 384 (2022), no. 3-4, 1275-1308.]
In this comment we point out some wrong statements in the paper by Inc and Cavlak, Phys. Scr. 78 (2008) 045008
This reply addresses concerns expressed in a comment (arXiv:2508.16689v1) on arXiv:submit/6841332 [physics.gen-ph] 29 Sep 2025 the paper given in the title (arXiv:2501.02022v2), hereafter referred to as the paper.
In this paper we implement the Darboux transformation, as well as an analogue of Crum's theorem, for a discrete version of Schr\"odinger equation. The technique is based on the use of first order operators intertwining two difference…
For the first time, Schr\"odinger equations with cubic and more complex nonlinearities containing the unknown function with constant delay are analyzed. The physical considerations that can lead to the appearance of a delay in such…
We analize the Nonlinear Schr\"odinger Equation.
Darboux transformation is one of the methods used in solving nonlinear evolution equation. Basically, the Darboux transformation is a linear algebra formulation of the solutions of the Zakharov-Shabat system of equations associated with the…
The results in the recently posted manuscript arXiv:math/0405153v3 are incorrect. The correct version of the aimed results is not original. The preprint contains material from references that are not properly quoted.
This results in this paper have been merged with the result in arXiv:1002.3763v1 The authors would like to withdraw this version. Please see arXiv:1008.5356v1 for the merged version.
Originally published as a Supplemental Appendix to Adjoint Equations in Stability Analysis, Annu. Rev. Fluid Mech. 46:493-517 (2014)
In this paper a nonlinear coupled Schrodinger system in the presence of mixed cubic and superlinear power laws is considered. A non standard numerical method is developed to approximate the solutions in higher dimensional case. The idea…
This article corrects two mistakes in the article "Coarse homology theories" [math.AT/0106183].
We comment on the Reply of G. Su and M. Suzuki [cond-mat/9808011] to our Comment [cond-mat/9807402] about the papers of G. Su [Phys. Rev. B 54, 8291 (1996)] and G. Su and M. Suzuki [Phys. Rev. B 57, 13367 (1998)]. The algebraic mistake…
The paper (as posted originally) contains several errors. It has been subsequently split into two papers, the corrected (and accepted for publication) versions appear in the archive as papers cs.CC/0503082 and cs.DM/0503083.
This is a Comment on the Article ``Aging, phase ordering and conformal invariance'' by M.Henkel, M.Pleimling, C.Godr\`eche and J.M.Luck [Phys.Rev.Lett. 87, 265701 (2001)].