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Relevant bibliographies by topics / Wronskian

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Journal articles

Academic literature on the topic 'Wronskian'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Wronskian"

1

Tarasov, V. "Completeness of the Bethe Ansatz for the Periodic Isotropic Heisenberg Model." Reviews in Mathematical Physics 30, no. 08 (2018): 1840018. http://dx.doi.org/10.1142/s0129055x18400184.

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For the periodic isotropic Heisenberg model with arbitrary spins and inhomogeneities, we describe the system of algebraic equations whose solutions are in bijection with eigenvalues of the transfer-matrix. The system describes pairs of polynomials with the given discrete Wronskian (Casorati determinant) and additional divisibility conditions on discrete Wronskians with multiple steps. If the polynomial of the smaller degree in the pair is coprime with the Wronskian, this system turns into the standard Bethe ansatz equations. Moreover, if the transfer-matrix is diagonalizable, then its spectrum

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2

Zhang, Da-Jun, Song-Lin Zhao, Ying-Ying Sun, and Jing Zhou. "Solutions to the modified Korteweg–de Vries equation." Reviews in Mathematical Physics 26, no. 07 (2014): 1430006. http://dx.doi.org/10.1142/s0129055x14300064.

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This is a continuation of [Notes on solutions in Wronskian form to soliton equations: Korteweg–de Vries-type, arXiv:nlin.SI/0603008]. In the present paper, we review solutions to the modified Korteweg–de Vries equation in terms of Wronskians. The Wronskian entry vector needs to satisfy a matrix differential equation set which contains complex operation. This fact makes the analysis of the modified Korteweg–de Vries to be different from the case of the Korteweg–de Vries equation. To derive complete solution expressions for the matrix differential equation set, we introduce an auxiliary matrix t

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3

Larsen, Mogens Esrom. "Wronskian Harmony." Mathematics Magazine 63, no. 1 (1990): 33. http://dx.doi.org/10.2307/2691509.

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4

Larsen, Mogens Esrom. "Wronskian Harmony." Mathematics Magazine 63, no. 1 (1990): 33–37. http://dx.doi.org/10.1080/0025570x.1990.11977481.

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5

Wang, Lei. "Triple Wronskian Representation of the Multi-Soliton Solutions for a Coupled GMNLS Equations." Advanced Materials Research 860-863 (December 2013): 2940–45. http://dx.doi.org/10.4028/www.scientific.net/amr.860-863.2940.

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In this paper, we mainly extend the notion of the Wronskian to a coupled GMNLS equations. Based on the N-fold Darboux transformation (DT), we present the triple Wronskian representation of the multi-soliton solutions for the coupled GMNLS equations. Di erent fromthe previous method, the triple Wronskian solutions can be obtained from the N -fold DT without substituting it into the bilinear equation. A signi cant advantage of such method is that it avoids guessing the Wroskian representation and Wronskian condition. Our approach could be applied other soliton equations with 3×3 spectral problem

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6

Pogudin, G. A. "Wronskian of derivations." Moscow University Mathematics Bulletin 66, no. 1 (2011): 47–49. http://dx.doi.org/10.3103/s0027132211010104.

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7

Amore, P., and F. M. Fernández. "Wronskian perturbation theory." European Physical Journal A 32, no. 1 (2007): 109–12. http://dx.doi.org/10.1140/epja/i2006-10358-3.

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8

Lü, DaZhao, YanYing Cui, ChangHe Liu, and ShangWen Wu. "Abundant Interaction Solutions of Sine-Gordon Equation." Journal of Applied Mathematics 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/842394.

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With the help of computer symbolic computation software (e.g.,Maple), abundant interaction solutions of sine-Gordon equation are obtained by means of a constructed Wronskian form expansion method. The method is based upon the forms and structures of Wronskian solutions of sine-Gordon equation, and the functions used in the Wronskian determinants do not satisfy linear partial differential equations. Such interaction solutions are difficultly obtained via other methods. And the method can be automatically carried out in computer.

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9

Domoshnitsky, Alexander, and Vladimir Raichik. "The Sturm Separation Theorem for Impulsive Delay Differential Equations." Tatra Mountains Mathematical Publications 71, no. 1 (2018): 65–70. http://dx.doi.org/10.2478/tmmp-2018-0006.

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Abstract Wronskian is one of the classical objects in the theory of ordinary differential equations. Properties of Wronskian lead to important conclusions on behaviour of solutions of delay equations. For instance, non-vanishing Wronskian ensures validity of the Sturm separation theorem (between two adjacent zeros of any solution there is one and only one zero of every other nontrivial linearly independent solution) for delay equations. We propose the Sturm separation theorem in the case of impulsive delay differential equations and obtain assertions about its validity.

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10

Zhang, Yi, and Kun Ma. "The triple Wronskian solutions to the variable-coefficient Manakov model." International Journal of Modern Physics B 30, no. 28n29 (2016): 1640031. http://dx.doi.org/10.1142/s0217979216400312.

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In this paper, the variable-coefficient Manakov model whose bilinear form exists is mainly discussed. Based on the Wronskian technique, the triple Wronskian form solutions are obtained and the interactions between the two solitons are investigated.

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