A Particle Method for the b-Equation

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References

[1] Camassa, R., Huang, J. and Lee, L. (2006) Integral and Integrable Algorithms for a Nonlinear Shallow-Water Wave Equation. Journal of Computational Physics, 216, 547-572. http://dx.doi.org/10.1016/j.jcp.2005.12.013

[2] Chertock, A., Du Toit, P. and Marsden, J. (2012) Integration of the EPDiff Equation by Particle Methods. ESAIM: Mathematical Modelling and Numerical Analysis, 46, 515-534. http://dx.doi.org/10.1051/m2an/2011054

[3] Chertock, A., Liu, J.G. and Pendleton, T. (2014) Elastic Collisions among Peakon Solutions for the Camassa-Holm Equation. Applied Numerical Mathematics, in press. http://dx.doi.org/10.1016/j.apnum.2014.01.001

[4] Matsuo, T. and Miyatake, Y. (2012) Conservative Finite Difference Schemes for Degasperis-Procesi Equation. Journal of Computational and Applied Mathematics, 236, 3728-3740. http://dx.doi.org/10.1016/j.cam.2011.09.004

[5] Camassa, R. and Lee, L. (2007) A Completely Integrable Particle Method for a Nonlinear Shallow-Water Wave Equation in Periodic Domains. Syst. Ser. A Math. Anal, 14, 1-5.

[6] Chertock, A., Liu, J.G. and Pendleton, T. (2012) Convergence of a Particle Method and Global Weak Solutions of a Family of Evolutionary PDEs. SIAM Journal on Numerical Analysis, 50, 1-21. http://dx.doi.org/10.1137/110831386

[7] Camassa, R., Huang, J. and Lee, L. (2005) On a Completely Integrable Numerical Scheme for a Nonlinear Shallow-Water Wave Equation. Journal of Nonlinear Mathematical Physics, 12, 146-162.
http://dx.doi.org/10.2991/jnmp.2005.12.s1.13

[8] Holden, H. and Raynaud, X. (2006) Convergence of a Finite Difference Scheme for the Camassa-Holm Equation. SIAM Journal on Numerical Analysis, 44, 1655-1680. http://dx.doi.org/10.1137/040611975