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Journal of Nonlinear Mathematical Physics Volume 14, 2007 - Issue 3
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Original Articles

Euler-Poincaré Formalism of (Two Component) Degasperis-Procesi and Holm-Staley type Systems

Partha Guha Max Planck Institute for Mathematics in the Sciences Inselstrasse 22, D-04103, Leipzig, GERMANY, S.N. Bose National Centre for Basic Sciences, JD Block, Sector-3, Salt Lake Calcutta-700098, India
Pages 398-429 | Received 12 Dec 2006, Accepted 15 Mar 2007, Published online: 21 Jan 2013

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Yong Chen, Hongjun Gao & Hua Luo. (2016) On the stochastic two-component b-family system. Stochastic Analysis and Applications 34:6, pages 1025-1044.
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Houria Triki, T. Hayat, Omar M. Aldossary & Anjan Biswas. (2011) Soliton and shock wave solutions to the Degasperis–Procesi equation with power law nonlinearity. Waves in Random and Complex Media 21:4, pages 543-553.
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Articles from other publishers (21)

Xing Wu, Cui Li & Jie Cao. (2022) Non-uniform continuity on initial data for the two-component b-family system in Besov space. Monatshefte für Mathematik 201:2, pages 547-563.
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Lijun Du & Xinglong Wu. (2023) The traveling wave solutions for a two-component b-family equations. Monatshefte für Mathematik.
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Lijun Du & Xinglong Wu. (2022) Global Well-Posedness of a Two–Component b–Family Equations in $$H^{s-1,p}({\mathbb {R}})\times H^{s,p}({\mathbb {R}})$$. Journal of Mathematical Fluid Mechanics 24:4.
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Xiaohuan Wang. (2022) On Initial Data Problem for a Periodic Two-Component b-Family System. Journal of Nonlinear Mathematical Physics 29:1, pages 171-185.
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Jiaopeng Yang, Rui Liu & Yiren Chen. (2020) Bifurcations of Solitary Waves of a Simple Equation. International Journal of Bifurcation and Chaos 30:09, pages 2050138.
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玲玲 邹. (2020) Bifurcations of Solitary Waves for a Class of Higher Order Nonlinear Equations. Advances in Applied Mathematics 09:08, pages 1273-1285.
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Zongguang Li & Rui Liu. (2019) Bifurcations and Exact Solutions in a Nonlinear Wave Equation. International Journal of Bifurcation and Chaos 29:07, pages 1950098.
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Jiaopeng Yang, Zongguang Li & Zhengrong Liu. (2018) The Existence and Bifurcation of Peakon and Anti-Peakon to the n-Degree b-Equation. International Journal of Bifurcation and Chaos 28:01, pages 1850014.
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Alexis Arnaudon. (2016) On a Lagrangian Reduction and a Deformation of Completely Integrable Systems. Journal of Nonlinear Science 26:5, pages 1133-1160.
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Bing Sun. (2016) An optimal distributed control problem of the viscous Degasperis–Procesi equation. IMA Journal of Mathematical Control and Information 33:3, pages 589-601.
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Yi-ren Chen, Wei-bo Ye & Rui Liu. (2016) The explicit periodic wave solutions and their limit forms for a generalized b-equation. Acta Mathematicae Applicatae Sinica, English Series 32:2, pages 513-528.
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Martin Bauer, Joachim Escher & Boris Kolev. (2015) Local and global well-posedness of the fractional order EPDiff equation on . Journal of Differential Equations 258:6, pages 2010-2053.
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Guangying Lv & Xiaohuan Wang. (2014) On the Cauchy problem for a two-component b-family system. Nonlinear Analysis: Theory, Methods & Applications 111, pages 1-14.
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Liqin Yu & Lixin Tian. (2014) Loop solutions, breaking kink (or anti-kink) wave solutions, solitary wave solutions and periodic wave solutions for the two-component Degasperis–Procesi equation. Nonlinear Analysis: Real World Applications 15, pages 140-148.
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Zhiqiang Wei, Yanyi Jin & Liangbing Jin. (2013) Infinite propagation speed for the two component b-family system. Journal of Inequalities and Applications 2013:1.
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Xiju Zong. (2012) Properties of the solutions to the two-component -family systems. Nonlinear Analysis: Theory, Methods & Applications 75:17, pages 6250-6259.
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Liu Rui. (2012) The explicit nonlinear wave solutions of the generalized $b$-equation. Communications on Pure and Applied Analysis 12:2, pages 1029-1047.
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Jingjing Liu & Zhaoyang Yin. (2011) On the Cauchy problem of a two-component b-family system. Nonlinear Analysis: Real World Applications 12:6, pages 3608-3620.
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RUI LIU. (2011) COEXISTENCE OF MULTIFARIOUS EXACT NONLINEAR WAVE SOLUTIONS FOR GENERALIZED b-EQUATION. International Journal of Bifurcation and Chaos 20:10, pages 3193-3208.
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Partha Guha. (2008) Virasoro Action on Pseudo-Differential Symbols and (Noncommutative) Supersymmetric Peakon Type Integrable Systems. Acta Applicandae Mathematicae 108:2, pages 215-234.
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Boris Kolev. (2009) Some geometric investigations on the Degasperis–Procesi shallow water equation. Wave Motion 46:6, pages 412-419.
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