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Journal of Nonlinear Mathematical Physics Volume 21, 2014 - Issue 3
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Original Articles

The Sylvester equation and integrable equations: I. The Korteweg-de Vries system and sine-Gordon equation

Dan-dan XuDepartment of Mathematics, Shanghai UniversityShanghai200444, P.R. China
,
Da-jun ZhangDepartment of Mathematics, Shanghai UniversityShanghai200444, P.R. ChinaCorrespondence[email protected]
&
Song-lin ZhaoDepartment of Mathematics, Zhejiang University of TechnologyHangzhou310023, P.R. China
Pages 382-406 | Received 03 Feb 2014, Accepted 23 Apr 2014, Published online: 24 Jun 2014

Citations (38)

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Tomas Nilson & Cornelia Schiebold. (2020) Solution formulas for the two-dimensional Toda lattice and particle-like solutions with unexpected asymptotic behaviour. Journal of Nonlinear Mathematical Physics 27:1, pages 57-94.
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Song-lin Zhao. (2019) Discrete potential Ablowitz–Kaup–Newell–Segur equation. Journal of Difference Equations and Applications 25:8, pages 1134-1148.
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Song-lin Zhao & Da-jun Zhang. (2019) Rational solutions to Q3δ in the Adler-Bobenko-Suris list and degenerations. Journal of Nonlinear Mathematical Physics 26:1, pages 107-132.
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Song-lin Zhao. (2016) A discrete negative AKNS equation: generalized Cauchy matrix approach. Journal of Nonlinear Mathematical Physics 23:4, pages 544-562.
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Articles from other publishers (34)

Shangshuai Li & Da-jun Zhang. (2024) Cauchy matrix structure and solutions of the spin-1 Gross–Pitaevskii equations. Communications in Nonlinear Science and Numerical Simulation 129, pages 107705.
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Aye Aye Cho, Jing Wang & Da-jun Zhang. (2023) Discretization of the modified Korteweg–de Vries–sine Gordon equation. Theoretical and Mathematical Physics 217:2, pages 1700-1716.
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Shangshuai Li, Changzheng Qu & Da-jun Zhang. (2023) Solutions to the SU( ) self-dual Yang–Mills equation . Physica D: Nonlinear Phenomena 453, pages 133828.
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Aye Aye Cho, Jing Wang & Da‐jun Zhang. (2023) A direct approach to the model of few‐optical‐cycle solitons beyond the slowly varying envelope approximation. Mathematical Methods in the Applied Sciences 46:8, pages 8518-8531.
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Zhihao Shi, Shangshuai Li & Da-jun Zhang. (2022) Cauchy matrix approach to the noncommutative Kadomtsev–Petviashvili equation with self-consistent sources. Theoretical and Mathematical Physics 213:3, pages 1686-1697.
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Хай-Цзин Сюй, Haijing Xu, Сун-Линь Чжао & Songlin Zhao. (2022) Решения, выраженные через матрицы Коши, для некоторых локальных и нелокальных комплексных уравненийCauchy matrix solutions of some local and nonlocal complex equations. Теоретическая и математическая физика Teoreticheskaya i Matematicheskaya Fizika 213:2, pages 234-267.
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Hai-jing Xu & Song-lin Zhao. (2022) Cauchy matrix solutions of some local and nonlocal complex equations. Theoretical and Mathematical Physics 213:2, pages 1513-1542.
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Hong-juan Tian, Xue-jing Feng & Wu-ming Liu. (2022) Extended KdV equations generated by squared eigenfunction symmetry. Applied Mathematics Letters 128, pages 107852.
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Shangshuai Li, Changzheng Qu, Xiangxuan Yi & Da‐jun Zhang. (2022) Cauchy matrix approach to the SU(2) self‐dual Yang–Mills equation. Studies in Applied Mathematics 148:4, pages 1703-1721.
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Мае-Бел Месфун, Maebel Mesfun, Сун-Линь Чжао & Songlin Zhao. (2022) Метод матриц Коши для полудискретных решеточных уравнений типа Кортевега-де ФризаCauchy matrix scheme for semidiscrete lattice Korteweg-de Vries-type equations. Теоретическая и математическая физика Teoreticheskaya i Matematicheskaya Fizika 211:1, pages 48-64.
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Maebel Mesfun & Song-Lin Zhao. (2022) Cauchy matrix scheme for semidiscrete lattice Korteweg–de Vries-type equations. Theoretical and Mathematical Physics 211:1, pages 483-497.
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Wei Feng & Songlin Zhao. (2022) The Sylvester Equation and Kadomtsev–Petviashvili System. Symmetry 14:3, pages 542.
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Шуай Чжан, Shuai Zhang, Сун-Линь Чжао, Songlin Zhao, Ин Ши & Ying Shi. (2022) Дискретное уравнение Абловица-Каупа-Ньюэлла-Сигура второго порядка и его модификацияDiscrete second-order Ablowitz-Kaup-Newell-Segur equation and its modified form. Теоретическая и математическая физика Teoreticheskaya i Matematicheskaya Fizika 210:3, pages 350-374.
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Shuai Zhang, Song-Lin Zhao & Ying Shi. (2022) Discrete second-order Ablowitz–Kaup–Newell–Segur equation and its modified form. Theoretical and Mathematical Physics 210:3, pages 304-326.
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V E Vekslerchik. (2022) Dark solitons of the Gross–Neveu model. Progress of Theoretical and Experimental Physics 2022:2.
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Lewa’ Alzaleq, Valipuram Manoranjan & Baha Alzalg. (2022) Exact Traveling Waves of a Generalized Scale-Invariant Analogue of the Korteweg–de Vries Equation. Mathematics 10:3, pages 414.
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Abdselam Silem, Hua Wu & Da-jun Zhang. (2021) Nonisospectral effects on generating localized waves. Communications in Theoretical Physics 73:11, pages 115002.
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Yue Yin & Wei Fu. (2021) Linear integral equations and two‐dimensional Toda systems. Studies in Applied Mathematics 147:3, pages 1146-1193.
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Guofei Zhang, Jingsong He, Lihong Wang & Dumitru Mihalache. (2021) Surfaces of revolution associated with the kink-type solutions of the SIdV equation. Differential Geometry and its Applications 74, pages 101711.
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Hong-Juan Tian & Da-Jun Zhang. (2020) Cauchy matrix structure of the Mel’nikov model of long–short wave interaction. Communications in Theoretical Physics 72:12, pages 125006.
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Weiguo Zhang, Yiwei Zhou & Ying-ying Sun. (2020) A lattice CKP equation expressed by the function . Applied Mathematics Letters 103, pages 106194.
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Hong-juan Tian & Da-jun Zhang. (2020) Cauchy matrix approach to integrable equations with self-consistent sources and the Yajima–Oikawa system. Applied Mathematics Letters 103, pages 106165.
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Danda Zhang, Da-Jun Zhang & Sen-Yue Lou. (2020) Lax Pairs of Integrable Systems in Bidifferential Graded Algebras*. Chinese Physics Letters 37:4, pages 040201.
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Aristophanes Dimakis & Folkert Müller-Hoissen. 2020. Algebraic Structures and Applications. Algebraic Structures and Applications 385 410 .
Guofei Zhang, Jingsong He, Lihong Wang & Dumitru Mihalache. (2019) Kink-type solutions of the SIdV equation and their properties. Royal Society Open Science 6:8, pages 191040.
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Wei Feng & Song-Lin Zhao. (2019) Cauchy Matrix Type Solutions for the Nonlocal Nonlinear Schrödinger Equation. Reports on Mathematical Physics 84:1, pages 75-83.
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Song-lin Zhao, Wei Feng & Yong-yang Jin. (2019) Discrete analogues for two nonlinear Schrödinger type equations. Communications in Nonlinear Science and Numerical Simulation 72, pages 329-341.
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V E Vekslerchik. (2019) Solitons of the (2+2)-dimensional Toda lattice. Journal of Physics A: Mathematical and Theoretical 52:4, pages 045202.
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Song-Lin Zhao. (2018) The Sylvester Equation and Integrable Equations: The Ablowitz—Kaup—Newell—Segur System. Reports on Mathematical Physics 82:2, pages 241-263.
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Wei Feng & Song-Lin Zhao. (2018) Oscillatory Solutions for Lattice Korteweg-de Vries-Type Equations. Zeitschrift für Naturforschung A 73:2, pages 91-98.
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Oleksandr Chvartatskyi & Folkert Müller-Hoissen. (2017) NLS breathers, rogue waves, and solutions of the Lyapunov equation for Jordan blocks. Journal of Physics A: Mathematical and Theoretical 50:15, pages 155204.
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Ying-ying Sun, Da-jun Zhang & Frank W. Nijhoff. (2017) The Sylvester equation and the elliptic Korteweg-de Vries system. Journal of Mathematical Physics 58:3.
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Song-lin Zhao & Ying-ying Sun. (2016) A Discrete Negative Order Potential Korteweg–de Vries Equation. Zeitschrift für Naturforschung A 71:12, pages 1151-1158.
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V E Vekslerchik. (2015) Soliton fay identities: II. Bright soliton case. Journal of Physics A: Mathematical and Theoretical 48:44, pages 445204.
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