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Journal of Nonlinear Mathematical Physics Volume 19, 2012 - Issue sup1
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Articles

INTEGRABLE MODELS FOR SHALLOW WATER WITH ENERGY DEPENDENT SPECTRAL PROBLEMS

ROSSEN IVANOV School of Mathematical Sciences, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland
&
TONY LYONS School of Mathematical Sciences, Dublin Institute of Technology, Kevin Street, Dublin 8, Ireland
Pages 72-88 | Published online: 04 Mar 2013

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Cheng Chen & Yao-Lin Jiang. (2019) Invariant solutions and conservation laws of the generalized Kaup–Boussinesq equation. Waves in Random and Complex Media 29:1, pages 138-152.
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Abdul-Majid Wazwaz. (2015) The generalized KaupߝBoussinesq equation: multiple soliton solutions. Waves in Random and Complex Media 25:4, pages 473-481.
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Articles from other publishers (11)

Vladimir Stefanov Gerdjikov & Aleksander Aleksiev Stefanov. (2023) Riemann–Hilbert Problems, Polynomial Lax Pairs, Integrable Equations and Their Soliton Solutions. Symmetry 15:10, pages 1933.
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B. A. Babajanov, A. Sh. Azamatov & R. B. Atajanova. (2023) Integration of the Kaup–Boussinesq system with time-dependent coefficients. Theoretical and Mathematical Physics 216:1, pages 961-972.
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Ruizhi Gong & Deng-Shan Wang. (2022) Formation of the undular bores in shallow water generalized Kaup–Boussinesq model. Physica D: Nonlinear Phenomena 439, pages 133398.
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Ruizhi Gong, Yuren Shi & Deng-Shan Wang. (2022) Linear stability of exact solutions for the generalized Kaup-Boussinesq equation and their dynamical evolutions. Discrete and Continuous Dynamical Systems 42:7, pages 3355.
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Jing Kang, Xiaochuan Liu, P. J. Olver & Changzheng Qu. (2020) Liouville correspondences between multicomponent integrable hierarchies. Theoretical and Mathematical Physics 204:1, pages 843-874.
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R K Gupta & Manjit Singh. (2019) On invariant analysis and conservation laws for degenerate coupled multi-KdV equations for multiplicity $$l = 3$$ l = 3. Pramana 92:5.
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Jack Haberlin & Tony Lyons. (2018) Solitons of shallow-water models from energy-dependent spectral problems. The European Physical Journal Plus 133:1.
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Alan Compelli & Rossen I. Ivanov. (2016) The Dynamics of Flat Surface Internal Geophysical Waves with Currents. Journal of Mathematical Fluid Mechanics 19:2, pages 329-344.
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Emrullah Yaşar & Sait San. (2016) A Procedure to Construct Conservation Laws of Nonlinear Evolution Equations. Zeitschrift für Naturforschung A 71:5, pages 475-480.
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Metin Gürses & Aslı Pekcan. (2014) Traveling wave solutions of degenerate coupled Korteweg-de Vries equation. Journal of Mathematical Physics 55:9, pages 091501.
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Abdul-Majid Wazwaz. (2013) Multiple soliton solutions for the Whitham–Broer–Kaup model in the shallow water small-amplitude regime. Physica Scripta 88:3, pages 035007.
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