T. I. Garagash, “About the modification of the Painlevé test for systems of nonlinear partial differential equations”, TMF, 100:3 (1994), 367–376; Theoret. and Math. Phys., 100:3 (1994), 1075

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Teoreticheskaya i Matematicheskaya Fizika, 1994, Volume 100, Number 3, Pages 367–376 (Mi tmf1655)

This article is cited in 32 scientific papers (total in 32 papers)

About the modification of the Painlevé test for systems of nonlinear partial differential equations

T. I. Garagash

Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (993 kB) Citations (32)

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Abstract: Following the formulation of [1] the Painlevé test is considered for the 2+1 dimensional model proposed in [2]. It is shown that for the model considered the standard ascending series procedure is correct only on the subset of solutions of the 1+1 dimensional reduction. The modified ascending series procedure is proposed giving a possibility to realize the procedure for a nonreduced case. Basing on this procedure, new representations of the Lax pair and the Backlund transformation are obtaioned. It is shown that the considered system is hamiltonian and some special (soliton's type) solutions are constructed.

Received: 14.10.1993

English version:
Theoretical and Mathematical Physics, 1994, Volume 100, Issue 3, Pages 1075–1081
DOI: https://doi.org/10.1007/BF01018572

Bibliographic databases:

Language: Russian

Citation: T. I. Garagash, “About the modification of the Painlevé test for systems of nonlinear partial differential equations”, TMF, 100:3 (1994), 367–376; Theoret. and Math. Phys., 100:3 (1994), 1075–1081

Citation in format AMSBIB

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https://www.mathnet.ru/eng/tmf/v100/i3/p367

This publication is cited in the following 32 articles:

Diana S. Maltseva, Roman O. Popovych, “Point-symmetry pseudogroup, Lie reductions and exact solutions of Boiti–Leon–Pempinelli system”, Physica D: Nonlinear Phenomena, 460 (2024), 134081
Stavros Kontogiorgis, Christodoulos Sophocleous, “The variable coefficient Boiti–Leon–Pempinelli and similar systems: The Lie symmetry approach”, Math Methods in App Sciences, 2024
Xin-Yi Gao, “Hetero-Bäcklund transformation, bilinear forms and multi-solitons for a (2＋1)-dimensional generalized modified dispersive water-wave system for the shallow water”, Chinese Journal of Physics, 2024
Serbay Duran, “Extractions of travelling wave solutions of (2 + 1)-dimensional Boiti–Leon–Pempinelli system via (Gʹ/G, 1/G)-expansion method”, Opt Quant Electron, 53:6 (2021)
Mukesh Kumar, Raj Kumar, Anshu Kumar, “Some More Invariant Solutions of (2 + 1)-Water Waves”, Int. J. Appl. Comput. Math, 7:1 (2021)
培源易, “New Traveling Wave Solutions for Boiti-Leon-Pempinelle Equation”, AAM, 07:12 (2018), 1537
Jun Liu, Gui Mu, Zhengde Dai, Hongying Luo, “Spatiotemporal deformation of multi-soliton to (2 + 1)-dimensional KdV equation”, Nonlinear Dyn, 83:1-2 (2016), 355
Jinxi Fei, Zhengyi Ma, Yuanming Chen, “Symmetry reduction and explicit solutions of the (2+1)-dimensional Boiti–Leon–Pempinelli system”, Applied Mathematics and Computation, 268 (2015), 432
Mukesh Kumar, Raj Kumar, Anshu Kumar, “Some more similarity solutions of the (2+1)-dimensional BLP system”, Computers & Mathematics with Applications, 70:3 (2015), 212
Xin-Yi Gao, “Comment on “Solitons, Bäcklund transformation, and Lax pair for the (2 + 1)-dimensional Boiti-Leon- Pempinelli equation for the water waves” [J. Math. Phys. 51, 093519 (2010)]”, Journal of Mathematical Physics, 56:1 (2015)
Ling Xu, Xuan Cheng, Chao-Qing Dai, “Discussions on equivalent solutions and localized structures via the mapping method based on Riccati equation”, Eur. Phys. J. Plus, 130:12 (2015)
Yun-Hu Wang and Hui Wang, “Symmetry analysis and CTE solvability for the (2+1)-dimensional Boiti–Leon–Pempinelli equation”, Phys. Scr., 89:12 (2014), 125203
Mukesh Kumar, Raj Kumar, “On New Similarity Solutions of the Boiti—Leon—Pempinelli System”, Commun. Theor. Phys., 61:1 (2014), 121
Ben Gao, Zhiyong Zhang, Yufu Chen, “Type-II hidden symmetry and nonlinear self-adjointness of Boiti–Leon–Pempinelli equation”, Communications in Nonlinear Science and Numerical Simulation, 19:1 (2014), 29
GUI MU, ZHENGDE DAI, ZHANHUI ZHAO, “Localized structures for (2+1)-dimensional Boiti–Leon–Pempinelli equation”, Pramana - J Phys, 81:3 (2013), 367
Shpilevoi A.A., Yurov A.V., Gritsenko V.A., “Nelineinye dissipativnye struktury kak model dvumernykh opticheskikh solitonov”, Vestnik Baltiiskogo federalnogo universiteta im. I. Kanta, 2012, no. 4, 14–20 Nonlinear dissipative structures as model of two-dimensional optic solitons
Chao-Qing Dai, Yue-Yue Wang, “Localized coherent structures based on variable separation solution of the (2+1)-dimensional Boiti–Leon–Pempinelli equation”, Nonlinear Dyn, 70:1 (2012), 189
İsmail Aslan, “Application of the Exp-function method to the (2+1)-dimensional Boiti–Leon–Pempinelli equation using symbolic computation”, International Journal of Computer Mathematics, 88:4 (2011), 747
Zheng Yang, Song-Hua Ma, Jian-Ping Fang, “Soliton excitations and chaotic patterns for the (2+1)-dimensional Boiti—Leon—Pempinelli system”, Chinese Phys. B, 20:6 (2011), 060506
Yan Jiang, Bo Tian, Wen-Jun Liu, Min Li, Pan Wang, Kun Sun, “Solitons, Bäcklund transformation, and Lax pair for the (2+1)-dimensional Boiti–Leon–Pempinelli equation for the water waves”, Journal of Mathematical Physics, 51:9 (2010)

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

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