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Journal of Nonlinear Mathematical Physics Volume 12, 2005 - Issue sup1: Special Issue in Honour of Francesco Calogero on the Occasion of His 70th Birthday
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Original Articles

A Class of Equations with Peakon and Pulson Solutions (with an Appendix by Harry Braden and John Byatt-Smith)

Darryl D Holm Computer and Computational Science Division Los Alamos National Laboratory, MS D413, NM 87545, Los Alamos, Sweden E-mail: [email protected]; Mathematics Department, Imperial College London, SW7 2AZ, U.K. E-mail: [email protected]
&
N W Hone Institute of Mathematics and Statistics, University of Kent, CT2 7NF, Canterbury, U.K. E-mail: [email protected]
Pages 380-394 | Published online: 21 Jan 2013

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Subham Dutta & Pralay Kumar Karmakar. (2023) A multi-order nonlinear meta-analysis of bifluidic fireball sheath fluctuations. Waves in Random and Complex Media 0:0, pages 1-27.
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A. Alexandrou Himonas, Curtis Holliman & Katelyn Grayshan. (2014) Norm Inflation and Ill-Posedness for the Degasperis-Procesi Equation. Communications in Partial Differential Equations 39:12, pages 2198-2215.
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Hailiang Liu. (2006) Wave Breaking in a Class of Nonlocal Dispersive Wave Equations. Journal of Nonlinear Mathematical Physics 13:3, pages 441-466.
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Articles from other publishers (38)

Runzhang Xu & Yanbing Yang. (2023) Local well-posedness and decay for some generalized shallow water equations. Journal of Differential Equations 367, pages 689-728.
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Efstathios G Charalampidis, Ross Parker, Panayotis G Kevrekidis & Stéphane Lafortune. (2023) The stability of the b-family of peakon equations. Nonlinearity 36:2, pages 1192-1217.
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Stéphane Lafortune & Dmitry E. Pelinovsky. (2022) Stability of smooth solitary waves in the -Camassa–Holm equation . Physica D: Nonlinear Phenomena 440, pages 133477.
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Aiyong Chen, Hao Yu & Xiaokai He. (2022) 2-Peakon Solutions and Non-uniqueness of the Fokas–Olver–Rosenau–Qiao Equation with Higher-Order Nonlinearity. Bulletin of the Malaysian Mathematical Sciences Society 45:6, pages 3401-3422.
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Subham Dutta & Pralay Kumar Karmakar. (2022) Fireball sheath instability. Journal of Astrophysics and Astronomy 43:2.
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Jean Avan, Luc Frappat & Eric Ragoucy. (2022) Integrable quadratic structures in peakon models. SciPost Physics 13:2.
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L. E. Barnes & A. N. W. Hone. (2022) Similarity reductions of peakon equations: the $$b$$-family. Theoretical and Mathematical Physics 212:2, pages 1149-1167.
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Hao Yu, Aiyong Chen & Kelei Zhang. (2021) Construction of 2-Peakon Solutions and Nonuniqueness for a Generalized mCH Equation. Advances in Mathematical Physics 2021, pages 1-10.
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Emil Novruzov. (2021) Construction of peakon-antipeakon solutions and ill-posedness for the b-family of equations. Journal of Differential Equations 272, pages 544-559.
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Yongki Lee. (2020) Wave breaking in a class of non-local conservation laws. Journal of Differential Equations 269:10, pages 8838-8854.
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Stephen C Anco & Elena Recio. (2019) A general family of multi-peakon equations and their properties. Journal of Physics A: Mathematical and Theoretical 52:12, pages 125203.
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Lijun Zhang, Jianming Zhang, Yuzhen Bai & Robert Hakl. (2019) EXPLICIT PEAKON SOLUTIONS TO A FAMILY OF WAVE-BREAKING EQUATIONS. Journal of Applied Analysis & Computation 9:5, pages 1987-1998.
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L.E. Barnes & A.N.W. Hone. (2019) Dynamics of conservative peakons in a system of Popowicz. Physics Letters A 383:5, pages 406-413.
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Yongki Lee. (2019) Thresholds for shock formation in traffic flow models with nonlocal-concave-convex flux. Journal of Differential Equations 266:1, pages 580-599.
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Minzhi Wei, Xianbo Sun & Hongying Zhu. (2018) BIFURCATIONS OF TRAVELING WAVE SOLUTIONS FOR A GENERALIZED CAMASSA-HOLM EQUATION. Journal of Applied Analysis & Computation 8:6, pages 1851-1862.
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A. Alexandrou Himonas, Katelyn Grayshan & Curtis Holliman. (2016) Ill-Posedness for the b-Family of Equations. Journal of Nonlinear Science 26:5, pages 1175-1190.
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A. Alexandrou Himonas & Dionyssios Mantzavinos. (2016) The initial value problem for a Novikov system. Journal of Mathematical Physics 57:7.
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A. S. Richardson, J. R. Angus, S. B. Swanekamp, I. M. Rittersdorf, P. F. Ottinger & J. W. Schumer. (2016) The effect of electron inertia in Hall-driven magnetic field penetration in electron-magnetohydrodynamics. Physics of Plasmas 23:5.
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Yongki Lee & Hailiang Liu. (2015) Threshold for shock formation in the hyperbolic Keller–Segel model. Applied Mathematics Letters 50, pages 56-63.
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María S. Bruzón, María L. Gandarias, Elena Recio & Stephen C. Anco. (2015) A nonlinear generalization of the Camassa-Holm equation with peakon solutions. A nonlinear generalization of the Camassa-Holm equation with peakon solutions.
Stephen C. Anco, Priscila Leal da Silva & Igor Leite Freire. (2015) A family of wave-breaking equations generalizing the Camassa-Holm and Novikov equations. Journal of Mathematical Physics 56:9.
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Rafael F. Barostichi, A. Alexandrou Himonas & Gerson Petronilho. 2015. Analysis and Geometry. Analysis and Geometry 59 68 .
John Holmes. (2014) Continuity properties of the data-to-solution map for the generalized Camassa–Holm equation. Journal of Mathematical Analysis and Applications 417:2, pages 635-642.
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Yongki Lee & Hailiang Liu. (2014) Thresholds for shock formation in traffic flow models with Arrhenius look-ahead dynamics. Discrete and Continuous Dynamical Systems 35:1, pages 323-339.
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A.N.W. Hone & S. Lafortune. (2014) Stability of stationary solutions for nonintegrable peakon equations. Physica D: Nonlinear Phenomena 269, pages 28-36.
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Baoqiang Xia & Zhijun Qiao. (2013) The N-kink, bell-shape and hat-shape solitary solutions of b-family equation in the case of . Physics Letters A 377:37, pages 2340-2342.
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Xianguo Geng & Hui Wang. (2013) Coupled Camassa–Holm equations, -peakons and infinitely many conservation laws. Journal of Mathematical Analysis and Applications 403:1, pages 262-271.
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A. Alexandrou Himonas & John Holmes. (2013) Hölder continuity of the solution map for the Novikov equation. Journal of Mathematical Physics 54:6.
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Lin Luo, Bao-Qiang Xia & Yu-Feng Cao. (2013) Peakon Solutions to Supersymmetric Camassa—Holm Equation and Degasperis—Procesi Equation. Communications in Theoretical Physics 59:1, pages 73-79.
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Katelyn Grayshan. (2013) Peakon solutions of the Novikov equation and properties of the data-to-solution map. Journal of Mathematical Analysis and Applications 397:2, pages 515-521.
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A Alexandrou Himonas & Curtis Holliman. (2012) The Cauchy problem for the Novikov equation. Nonlinearity 25:2, pages 449-479.
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N. A. Kudryashov & D. I. Sinel’shchikov. (2010) Nonlinear waves in liquids with gas bubbles with account of viscosity and heat transfer. Fluid Dynamics 45:1, pages 96-112.
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Xianguo Geng & Bo Xue. (2009) An extension of integrable peakon equations with cubic nonlinearity. Nonlinearity 22:8, pages 1847-1856.
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Lixin Tian, Yuexia Chen, Xiuping Jiang & Limeng Xia. (2009) Low-regularity solutions of the periodic Fornberg–Whitham equation. Journal of Mathematical Physics 50:7.
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Lixin Tian & Shujuan Liang. (2009) Global well posedness and limit behavior of the solutions to the viscous Degasperis?Procesi equation. Journal of Mathematical Physics 50:3, pages 033503.
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Andrew N W Hone & Jing Ping Wang. (2008) Integrable peakon equations with cubic nonlinearity. Journal of Physics A: Mathematical and Theoretical 41:37, pages 372002.
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Jennifer Kohlenberg, Hans Lundmark & Jacek Szmigielski. (2007) The inverse spectral problem for the discrete cubic string. Inverse Problems 23:1, pages 99-121.
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E.J. Parkes & V.O. Vakhnenko. (2005) Explicit solutions of the Camassa?Holm equation. Chaos, Solitons & Fractals 26:5, pages 1309-1316.
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