Stability of Multipeakons
Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 4, pp. 1517-1532.
@article{AIHPC_2009__26_4_1517_0,
     author = {El Dika, Khaled and Molinet, Luc},
     title = {Stability of {Multipeakons}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1517--1532},
     publisher = {Elsevier},
     volume = {26},
     number = {4},
     year = {2009},
     doi = {10.1016/j.anihpc.2009.02.002},
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     zbl = {1171.35459},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2009.02.002/}
}
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El Dika, Khaled; Molinet, Luc. Stability of Multipeakons. Annales de l'I.H.P. Analyse non linéaire, Tome 26 (2009) no. 4, pp. 1517-1532. doi : 10.1016/j.anihpc.2009.02.002. http://www.numdam.org/articles/10.1016/j.anihpc.2009.02.002/

[1] Beals R., Sattinger D. H., Szmigielski J., Multipeakons and the Classical Moment Problem, Adv. Math. 154 (2) (2000) 229-257. | MR | Zbl

[2] Benjamin T. B., The Stability of Solitary Waves, Proc. R. Soc. Lond. Ser. A 328 (1972) 153-183. | MR

[3] Bressan A., Constantin A., Global Conservative Solutions of the Camassa-Holm Equation, Arch. Ration. Mech. Anal. 187 (2007) 215-239. | MR | Zbl

[4] Bressan A., Constantin A., Global Dissipative Solutions of the Camassa-Holm Equation, J. Anal. Appl. 5 (2007) 1-27. | MR | Zbl

[5] Camassa R., Holm D., An Integrable Shallow Water Equation With Peaked Solitons, Phys. Rev. Lett. 71 (1993) 1661-1664. | MR | Zbl

[6] Camassa R., Holm D., Hyman J., An New Integrable Shallow Water Equation, Adv. Appl. Mech. 31 (1994). | Zbl

[7] Constantin A., On the Scattering Problem for the Camassa-Holm Equation, Proc. R. Soc. Lond. Ser. A 457 (2001) 953-970. | MR | Zbl

[8] Constantin A., The Trajectories of Particles in Stolkes Waves, Invent. Math. 166 (2006) 523-535. | MR | Zbl

[9] Constantin A., Escher J., Particle Trajectories in Solitary Waves, Bull. Amer. Math. Soc. (N.S.) 44 (2007) 423-431. | MR | Zbl

[10] Constantin A., Gerdjikov V., Ivanov R., Inverse Scattering Transform for the Camassa-Holm Equation, Inverse Problems 22 (2006) 2197-2207. | MR | Zbl

[11] Constantin A., Strauss W., Stability of Peakons, Comm. Pure Appl. Math. 53 (2000) 603-610. | MR | Zbl

[12] Constantin A., Strauss W., Stability of the Camassa-Holm Solitons, J. Nonlinear Sci. 12 (2002) 415-422. | MR | Zbl

[13] Constantin A., Molinet L., Global Weak Solutions for a Shallow Water Equation, Comm. Math. Phys. 211 (2000) 45-61. | MR | Zbl

[14] Constantin A., Molinet L., Orbital Stability of Solitary Waves for a Shallow Water Equation, Phys. D 157 (2001) 75-89. | MR | Zbl

[15] Dai H.-H., Model Equations for Nonlinear Dispersive Waves in Compressible Mooney-Rivlin Rod, Acta Mech. Sin. 127 (1998) 293-308. | MR | Zbl

[16] Danchin R., A Few Remarks on the Camassa-Holm Equation, Differential Integral Equations 14 (2001) 953-980. | MR | Zbl

[17] El Dika K., Smoothing Effect of the Generalized BBM Equation for Localized Solutions Moving to the Right, Discrete Contin. Dyn. Syst. 12 (2005) 973-982. | MR

[18] El Dika K., Martel Y., Stability of N Solitary Waves for the Generalized BBM Equations, Dyn. Partial Differ. Equ. 1 (2004) 401-437. | MR | Zbl

[19] El Dika K., Molinet L., Exponential Decay of H 1 -Localized Solutions and Stability of the Train of N Solitary Waves for the Camassa-Holm Equation, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 365 (2007) 2313-2331. | MR | Zbl

[20] Fokas A. S., Fuchssteiner B., Symplectic Structures, Their Bäcklund Transformation and Hereditary Symmetries, Phys. D 4 (1981) 47-66. | MR

[21] Grillakis M., Shatah J., Strauss W., Stability Theory of Solitary Waves in the Presence of Symmetry, J. Funct. Anal. 74 (1987) 160-197. | MR | Zbl

[22] Holden H., Raynaud X., A Convergent Numerical Scheme for the Camassa-Holm Equation Based on Multipeakons, Discrete Contin. Dyn. Syst. 14 (3) (2006) 505-523. | MR | Zbl

[23] Johnson R. S., Camassa-Holm, Korteweg-De Vries and Related Models for Water Waves, J. Fluid Mech. 455 (2002) 63-82. | MR | Zbl

[24] Martel Y., Merle F., Tsai T.-P., Stability and Asymptotic Stability in the Energy Space of the Sum of N Solitons for Subcritical GKdV Equations, Comm. Math. Phys. 231 (2002) 347-373. | MR | Zbl

[25] Martel Y., Merle F., Tsai T.-P., Stability in H 1 of the Sum of K Solitary Waves for Some Nonlinear Schrödinger Equations, Duke Math. J. 133 (3) (2006) 405-466. | MR | Zbl

[26] Molinet L., On Well-Posedness Results for Camassa-Holm Equation on the Line: a Survey, J. Nonlinear Math. Phys. 11 (2004) 521-533. | MR | Zbl

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