J. C. Nimmo, C. R. Gilson, Ya. Ohta, “Applications of Darboux transformations to the self-dual Yang–Mills equations”, TMF, 122:2 (2000), 284–293; Theoret. and Math. Phys., 122:2 (2000), 239

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Teoreticheskaya i Matematicheskaya Fizika, 2000, Volume 122, Number 2, Pages 284–293
DOI: https://doi.org/10.4213/tmf1932 (Mi tmf1932)

This article is cited in 47 scientific papers (total in 47 papers)

Applications of Darboux transformations to the self-dual Yang–Mills equations

J. C. Nimmo^a, C. R. Gilson^a, Ya. Ohta^b

^a University of Glasgow
^b Hiroshima University

Full-text PDF (224 kB) Citations (47)

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DOI: https://doi.org/10.4213/tmf1932

Abstract: The linear problem associated with the self-dual Yang–Mills equations is covariant with respect to Darboux and binary Darboux transformations of almost classical type. This technique is used to construct solutions of the problem in the form of Wronskian-like and Gramm-like determinants. The self-dual conditions can be properly realized for only the latter type of solutions.

English version:
Theoretical and Mathematical Physics, 2000, Volume 122, Issue 2, Pages 239–246
DOI: https://doi.org/10.1007/BF02551200

Bibliographic databases:

Language: Russian

Citation: J. C. Nimmo, C. R. Gilson, Ya. Ohta, “Applications of Darboux transformations to the self-dual Yang–Mills equations”, TMF, 122:2 (2000), 284–293; Theoret. and Math. Phys., 122:2 (2000), 239–246

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf1932

https://doi.org/10.4213/tmf1932

https://www.mathnet.ru/eng/tmf/v122/i2/p284

This publication is cited in the following 47 articles:

Hong-Qian Sun, Shou-Feng Shen, Zuo-Nong Zhu, “Asymptotic Analysis of Soliton Solutions for the Coupled Modified Complex Short Pulse Equation by Binary Darboux Transformation”, J Nonlinear Sci, 35:3 (2025)
Shangshuai Li, Masashi Hamanaka, Shan-Chi Huang, Da-Jun Zhang, “Soliton resonances in four dimensional Wess-Zumino-Witten model”, Phys. Rev. D, 111:8 (2025)
H W A Riaz, J Lin, “The quasi-Gramian solution of a non-commutative extension of the higher-order nonlinear Schrödinger equation”, Commun. Theor. Phys., 76:3 (2024), 035005
Halis Yilmaz, “Quasi-Grammian solutions of the coupled Gerdjikov–Ivanov equation”, Wave Motion, 124 (2024), 103245
A. Inam, M. ul Hassan, “Quasi-Grammian loop dynamics of a multicomponent semidiscrete short pulse equation”, Theoret. and Math. Phys., 220:3 (2024), 1530–1555
A. Inam, M. ul Hassan, “Quasi-Grammian soliton and kink dynamics of an $M$ -component semidiscrete coupled integrable system”, Theoret. and Math. Phys., 221:1 (2024), 1650–1674
Shangshuai Li, Da-jun Zhang, “Direct linearization of the SU(2) anti-self-dual Yang-Mills equation in various spaces”, Journal of Geometry and Physics, 2024, 105351
H. Wajahat A. Riaz, “Noncommutative generalization and quasi-Gramian solutions of the Hirota equation”, Theoret. and Math. Phys., 214:2 (2023), 194–206
Lian-li Feng, Zuo-nong Zhu, “Darboux Transformation and Soliton Solutions for a Nonlocal Two-Component Complex Modified Korteweg–de Vries Equation”, J Nonlinear Math Phys, 30:3 (2023), 1011
Masashi Hamanaka, Shan-Chi Huang, Hiroaki Kanno, “Solitons in openN= 2 string theory”, Progress of Theoretical and Experimental Physics, 2023:4 (2023)
Shangshuai Li, Changzheng Qu, Da-jun Zhang, “Solutions to the SU(N) self-dual Yang–Mills equation”, Physica D: Nonlinear Phenomena, 453 (2023), 133828
Hamanaka M. Huang Sh.-Ch., “Multi-Soliton Dynamics of Anti-Self-Dual Gauge Fields”, J. High Energy Phys., 2022, no. 1, 039
Li Sh., Qu Ch., Yi X., Zhang D.-j., “Cauchy Matrix Approach to the Su(2) Self-Dual Yang-Mills Equation”, Stud. Appl. Math., 148:4 (2022), 1703–1721
Halis Yilmaz, “Binary Darboux transformation for the Gerdjikov–Ivanov equation”, Wave Motion, 113 (2022), 102991
Halis Yilmaz, “Darboux Transformation for the Hirota Equation”, Z. mat. fiz. anal. geom., 18:1 (2022), 136
Hong-Qian Sun, Zuo-Nong Zhu, “Darboux transformation and soliton solutions of the spatial discrete coupled complex short pulse equation”, Physica D: Nonlinear Phenomena, 436 (2022), 133312
Caiqin Song, Chen-Chen Fu, Zuo-Nong Zhu, “The two-component complex coupled integrable dispersionless equations: Darboux transformation and soliton solutions”, Partial Differential Equations in Applied Mathematics, 6 (2022), 100436
Gilson C.R. Hamanaka M. Huang Sh.-Ch. Nimmo J.J.C., “Soliton Solutions of Noncommutative Anti-Self-Dual Yang-Mills Equations”, J. Phys. A-Math. Theor., 53:40 (2020), 404002
Hamanaka M. Huang Sh.-Ch., “New Soliton Solutions of Anti-Self-Dual Yang-Mills Equations”, J. High Energy Phys., 2020, no. 10, 101
Amjad Z., Haider B., “Quasi-Grammian Solutions of the Generalized Heisenberg Magnet Model”, Can. J. Phys., 98:3 (2020), 303–311

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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