参考文献/References:
[1] Constantin A,Kolev B.Geodesic flow on the diffeomorphism group of the circle[J].Comment Math Helv,2003,78(4):787-804.
[2] Camassa R,Holm D.An integrable shallow water equation with peaked soliton[J].Phys Rev Lett,1993,71:1661-1664.
[3] Bressan A,Constantin A.Global conservative solutions of the Camassa-Holm equation[J].Arch Ration Mech Anal,2007,183(2):215-239.
[4] Coclite G M,Holden H,Karlsen K H.Wellposedness of solutions of a parabolic-elliptic system[J].Discrete Contin Dyn Syst,2005,13(3):659-682.
[5] Constantin A,Escher J.Global existence and blow-up for a shallow water equation[J].Ann Sc Norm Super Pisa CI Sci,1998,26(2):303-328.
[6] Constantin A,Escher J.Global weak solutions for a shallow water equation[J].Indiana Univ Math J,1998,47(4):1527-1545.
[7] Constantin A,Escher J.On the structure of a family of quasi-linear equations arising in shallow water theory[J].Math Ann,1998,312(3):403-416.
[8] Constantin A,Escher J.Wave breaking for nonlinear nonlocal shallow water equations[J].Acta Math,1998,181(2):229-243.
[9] Constantin A,Escher J.Well-posedness,global existence,and blowup phenomena for a periodic quasi-linear hyperbolic equation[J].Comm Pure Appl Math,1998,51(5):475-504.
[10] Constantin A,Molinet L.Global weak solutions for a shallow water equation[J].Comm Math Phys,2000,211(1):45-61.
[11] Constantin A,Molinet L.Orbital stability of solitary waves for a shallow water equation[J].Commun Math Phys,2001,157(1):75-89.
[12] Constantin A,Strauss W A.Stability of peakons[J].Comm Pure Appl Math,2000,53(5):603-610.
[13] Ding Danping,Tian Lixin,Xu Gang.The study on solutions to Camassa-Holm equation with weak dissipation[J].Commun Pure Appl Anal,2006,5(3):483-492.
[14] Holden H,Raynaud X.Periodic conservative solutions of the Camassa-Holm equation[J].Ann Inst Fourier,2008,58(3):945-988.
[15] Tian Lixin,Fang Guochang,Gui Guilong.Well-posedness and blow-up for an integrable shallow water equation with strong dispersive term[J].Int J Nonlinear Sci,2006,1(1):3-13.
[16] Xin Zhouping,Zhang Ping.On the weak solutions to a shallow water equation[J].Comm Pure Appl Math,2000,53(11):1411-1433.
[17] Coclite G M,Holden H,Karlsen K H.Well-posedness of Higher-order Camassa-Holm equations[J].J Differential Equations,2009,246(3):929-963.
[18] Ding Danping,Lv Peng.Conservative solutions for higher-order Camassa-Holm equation[J].J Math Phys,2010,51:072701.
[19] Coclite G M,di Ruvo L.A note on the convergence of the solution of the high order Camassa-Holm equation to the entropy ones of a scalar conservation law[J].Discrete Contin Dyn Syst,2017,37(3):1247-1282.
[20] Ding Danping.Traveling solutions and evolution properties of the higher order Camassa-Holm equation[J].Nonlinear Anal,2017,152:1-11.
[21] Martel Y,Merle F.Instability of solitons for the critical generalized Korteweg-de Vries equation[J].Geom Funct Anal,2001,11(1):74-123.