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Journal of Nonlinear Mathematical Physics Volume 20, 2013 - Issue 1
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Original Articles

On the Discretization of the Coupled Integrable Dispersionless Equations

Luc Vinet Centre de Recherches Mathématiques, Université de Montréal, C.P.6128, Centre-ville Station, Montréal, Québec, H3C 3J7, CanadaCorrespondence[email protected]
&
Guo-Fu Yu Centre de Recherches Mathématiques, Université de Montréal, C.P.6128, Centre-ville Station, Montréal, Québec, H3C 3J7, Canada; Department of Mathematics, Shanghai Jiao Tong University, Shanghai, 200240, P.R. China
Pages 106-125 | Received 04 Aug 2012, Accepted 18 Jan 2013, Published online: 05 Apr 2013

Citations (19)

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Guo-Fu Yu & Yingnan Zhang. (2019) Integrable discretization and numerical simulations of the generalized coupled integrable dispersionless equations. Journal of Difference Equations and Applications 25:3, pages 408-429.
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Articles from other publishers (18)

A. H. Abdel Kader, F. El Bialy, H. M. Nour & M. S. Abdel Latif. (2023) Some new soliton solutions of a semi-discrete fractional complex coupled dispersionless system. Scientific Reports 13:1.
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Zhe Lin & Xiao-Yong Wen. (2022) Modulational instability and position controllable discrete rogue waves with interaction phenomena in the semi-discrete complex coupled dispersionless system. Wave Motion 112, pages 102932.
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Wei-Guo Zhang, Meng-Yu Wang & Caiqin Song. (2021) Soliton solutions of the semi-discrete complex coupled dispersionless integrable system. Applied Mathematics Letters 113, pages 106859.
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Fangcheng Fan, Shaoyun Shi & Zhiguo Xu. (2020) Positive and negative integrable lattice hierarchies: Conservation laws and fold Darboux transformations . Communications in Nonlinear Science and Numerical Simulation 91, pages 105453.
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Fangcheng Fan, Shaoyun Shi & Zhiguo Xu. (2020) Conservation laws and Darboux transformations for a 3-coupled integrable lattice equations. Modern Physics Letters B 34:21, pages 2050218.
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H. Sarfraz, Y. Hanif & U. Saleem. (2019) On $$\varvec{\mathcal {PT}}$$-symmetric semi-discrete coupled integrable dispersionless system. Nonlinear Dynamics 99:3, pages 2409-2419.
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Ying-Nan Zhang, Hong-Qian He, Guo-Fu Yu & Yi-Jun Dong. (2020) Integrable discretizations and numerical simulation for a modified coupled integrable dispersionless equation. Applied Mathematics and Computation 364, pages 124666.
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H.Wajahat A. Riaz & Mahmood ul Hassan. (2017) Darboux transformation of a semi-discrete coupled dispersionless integrable system. Communications in Nonlinear Science and Numerical Simulation 48, pages 387-397.
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Yingnan Zhang & Lixin Tian. (2016) An integrable semi-discretization of the Boussinesq equation. Physics Letters A 380:43, pages 3575-3582.
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Sen-Yue Lou & Guo-Fu Yu. (2016) A generalization of the coupled integrable dispersionless equations. Mathematical Methods in the Applied Sciences 39:14, pages 4025-4034.
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Hengchun Hu, Xiao Hu & Bao-Feng Feng. (2016) Nonlocal Symmetry and Consistent Tanh Expansion Method for the Coupled Integrable Dispersionless Equation. Zeitschrift für Naturforschung A 71:3, pages 235-240.
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Shoufeng Shen, Bao-Feng Feng & Yasuhiro Ohta. (2016) From the Real and Complex Coupled Dispersionless Equations to the Real and Complex Short Pulse Equations. Studies in Applied Mathematics 136:1, pages 64-88.
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G.-F. Yu. (2015) Discrete Analogues of a Negative Order AKNS Equation. Studies in Applied Mathematics 135:2, pages 117-138.
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Guo-Fu Yu & Zong-Wei Xu. (2015) Dynamics of a differential-difference integrable -dimensional system . Physical Review E 91:6.
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YingNan Zhang, XiangKe Chang, Juan Hu, XingBiao Hu & Hon-Wah Tam. (2014) Integrable discretization of soliton equations via bilinear method and Bäcklund transformation. Science China Mathematics 58:2, pages 279-296.
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Bao-Feng Feng, Kenichi Maruno & Yasuhiro Ohta. (2014) Self-adaptive moving mesh schemes for short pulse type equations and their Lax pairs. Pacific Journal of Mathematics for Industry 6:1.
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Luc Vinet & Guo-Fu Yu. (2013) Discrete analogues of the generalized coupled integrable dispersionless equations. Journal of Physics A: Mathematical and Theoretical 46:17, pages 175205.
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Zhe Lin & Xiao-Yong Wen. (2022) Modulational Instability and Position Controllable Discrete Rogue Waves with Interaction Phenomena in the Semi-Discrete Complex Coupled Dispersionless System. SSRN Electronic Journal.
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