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Higherorder shallow water equations and the CamassaHolm equation
1.  School of Mathematics and Maxwell Institute for Mathematical Sciences, The King's Buildings, University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom 
[1] 
Stephen C. Anco, Elena Recio, María L. Gandarias, María S. Bruzón. A nonlinear generalization of the CamassaHolm equation with peakon solutions. Conference Publications, 2015, 2015 (special) : 2937. doi: 10.3934/proc.2015.0029 
[2] 
Min Zhu, Shuanghu Zhang. Blowup of solutions to the periodic modified CamassaHolm equation with varying linear dispersion. Discrete & Continuous Dynamical Systems  A, 2016, 36 (12) : 72357256. doi: 10.3934/dcds.2016115 
[3] 
Min Zhu, Ying Wang. Blowup of solutions to the periodic generalized modified CamassaHolm equation with varying linear dispersion. Discrete & Continuous Dynamical Systems  A, 2017, 37 (1) : 645661. doi: 10.3934/dcds.2017027 
[4] 
Delia IonescuKruse. Variational derivation of the CamassaHolm shallow water equation with nonzero vorticity. Discrete & Continuous Dynamical Systems  A, 2007, 19 (3) : 531543. doi: 10.3934/dcds.2007.19.531 
[5] 
Yongsheng Mi, Boling Guo, Chunlai Mu. On an $N$Component CamassaHolm equation with peakons. Discrete & Continuous Dynamical Systems  A, 2017, 37 (3) : 15751601. doi: 10.3934/dcds.2017065 
[6] 
Helge Holden, Xavier Raynaud. Dissipative solutions for the CamassaHolm equation. Discrete & Continuous Dynamical Systems  A, 2009, 24 (4) : 10471112. doi: 10.3934/dcds.2009.24.1047 
[7] 
Zhenhua Guo, Mina Jiang, Zhian Wang, GaoFeng Zheng. Global weak solutions to the CamassaHolm equation. Discrete & Continuous Dynamical Systems  A, 2008, 21 (3) : 883906. doi: 10.3934/dcds.2008.21.883 
[8] 
Milena Stanislavova, Atanas Stefanov. Attractors for the viscous CamassaHolm equation. Discrete & Continuous Dynamical Systems  A, 2007, 18 (1) : 159186. doi: 10.3934/dcds.2007.18.159 
[9] 
Defu Chen, Yongsheng Li, Wei Yan. On the Cauchy problem for a generalized CamassaHolm equation. Discrete & Continuous Dynamical Systems  A, 2015, 35 (3) : 871889. doi: 10.3934/dcds.2015.35.871 
[10] 
Yu Gao, JianGuo Liu. The modified CamassaHolm equation in Lagrangian coordinates. Discrete & Continuous Dynamical Systems  B, 2018, 23 (6) : 25452592. doi: 10.3934/dcdsb.2018067 
[11] 
Yongsheng Mi, Boling Guo, Chunlai Mu. Persistence properties for the generalized CamassaHolm equation. Discrete & Continuous Dynamical Systems  B, 2020, 25 (5) : 16231630. doi: 10.3934/dcdsb.2019243 
[12] 
Li Yang, Zeng Rong, Shouming Zhou, Chunlai Mu. Uniqueness of conservative solutions to the generalized CamassaHolm equation via characteristics. Discrete & Continuous Dynamical Systems  A, 2018, 38 (10) : 52055220. doi: 10.3934/dcds.2018230 
[13] 
Yongsheng Mi, Chunlai Mu. On a threeComponent CamassaHolm equation with peakons. Kinetic & Related Models, 2014, 7 (2) : 305339. doi: 10.3934/krm.2014.7.305 
[14] 
Shouming Zhou, Chunlai Mu. Global conservative and dissipative solutions of the generalized CamassaHolm equation. Discrete & Continuous Dynamical Systems  A, 2013, 33 (4) : 17131739. doi: 10.3934/dcds.2013.33.1713 
[15] 
Shihui Zhu. Existence and uniqueness of global weak solutions of the CamassaHolm equation with a forcing. Discrete & Continuous Dynamical Systems  A, 2016, 36 (9) : 52015221. doi: 10.3934/dcds.2016026 
[16] 
Feng Wang, Fengquan Li, Zhijun Qiao. On the Cauchy problem for a higherorder μCamassaHolm equation. Discrete & Continuous Dynamical Systems  A, 2018, 38 (8) : 41634187. doi: 10.3934/dcds.2018181 
[17] 
Danping Ding, Lixin Tian, Gang Xu. The study on solutions to CamassaHolm equation with weak dissipation. Communications on Pure & Applied Analysis, 2006, 5 (3) : 483492. doi: 10.3934/cpaa.2006.5.483 
[18] 
Priscila Leal da Silva, Igor Leite Freire. An equation unifying both CamassaHolm and Novikov equations. Conference Publications, 2015, 2015 (special) : 304311. doi: 10.3934/proc.2015.0304 
[19] 
Stephen Anco, Daniel Kraus. Hamiltonian structure of peakons as weak solutions for the modified CamassaHolm equation. Discrete & Continuous Dynamical Systems  A, 2018, 38 (9) : 44494465. doi: 10.3934/dcds.2018194 
[20] 
Shaoyong Lai, Qichang Xie, Yunxi Guo, YongHong Wu. The existence of weak solutions for a generalized CamassaHolm equation. Communications on Pure & Applied Analysis, 2011, 10 (1) : 4557. doi: 10.3934/cpaa.2011.10.45 
2018 Impact Factor: 1.008
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