[1] Dai H H. Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod. Acta Mech, 1998, 127(1--4): 193--207
[2] Dai H H, Huo Y. Solitary shock waves and other travelling waves in a general compressible hyperelastic rod. R Soc Lond A, 1994, 456: 331--363
[3] Camassa R, Holm D. An integrable shallow water equation with peaked solitons. Phys Rev Letter, 1993, 71: 1661--1664
[4] Johnson R S. Camassa-Holm, Korteweg-de Vries and related models for water waves. J Fluid Mech, 2002, 455: 63--82
[5] Constantin A, Kolev B. Geodesic flow on the diffeomorphism group of the circle. Comment Math Helv, 2003, 78(4): 787--804
[6] Constantin A, Kolev B. On the geometric approach to the motion of inertial mechanical systems. J Phys A, 2002, 35(32): R51--R79
[7] Constantin A. On the inverse spectral problem for the Camassa-Holm equation. J Funct Anal, 1998, 155: 352--363
[8] Constantin A, McKean H P. A shallow water equation on the circle. Comm Pure Appl Math, 1999, 52(8): 949--982
[9] Beals R, Sattinger D, Szmigielski J. Acoustic scattering and the extended Korteweg-de Vries hierarchy. Adv
Math,1998, 140: 190--206
[10] Constantin A. On the scattering problem for the Camassa-Holm equation. Proc Roy Soc London, Ser A, 2001, 457: 953--970
[11] Constantin A, Gerdjikov V, Ivanov R. Inverse scattering transform fot the Camassa-Holm equation. Inverse
Problems, 2006, 22: 2197--2207
[12] Shkoller S. Geometry and curvature of diffeomorphism groups with H1 metric and mean hydrodynamics. J Funct Anal,1998, 160(1): 337--365
[13] Li Y, Olver P. Well-posedness and blow-up solutions for an integrable nonlinear dispersive model wave
equation. J Differential Equations, 2000, 162: 27--63
[14] Misiolek G. Classical solutions of the periodic Camassa-Holm equation. Geom Funct Anal, 2002, 12(5): 1080--1104
[15] Molinet L. On well-posedness results for Camassa-Holm equation on the line: a survey. J Nonlinear Math Phys, 2004, 11(4): 521--533
[16] Bressan A, Constantin A. Global conservative solutions of the Camassa-Holm equation. Arch Rat Mrch Anal, 2007, 183: 215--239
[17] Constantin A, Escher J. Well-posedness, global existence and blow-up phenomena for a periodic quasi-linear hyperbolic equation. Comm Pure Appl Math, 1998, 51: 475--504
[18] Constantin A, Escher J. Wave breaking for nonlinear nonlocal shallow water equations. Acta Math, 1998, 181: 229--243
[19] McKean H P. Breakdown of a shallow water equation. Asian J Math, 1998, 2(4): 867--874
[20] Zhou Y. Wave breaking for a periodic shallow water equation. J Math Anal Appl, 2004, 290: 591--604
[21] Xin Z, Zhang P. On the weak solution to a shallow water equation. Comm Pure Appl Math, 2000, 53: 1411--1433
[22] Constantin A. Existence of permanent and breaking waves for a shallow water equation: a geometric approach. Ann Inst Fourier (Grenoble), 2000, 50(2): 321--362
[23] Beals R, Sattinger D, Szmigielski J. Multi-peakons and a theorem of Stieltjes. Inverse Problems, 1999, 15(1): L1--L4
[24] Constantin A, Strauss W. Stability of peakons. Comm Pure Appl Math, 2000, 53(5): 603--610
[25] Constantin A, Strauss W. Stability of a class of solitary waves in compressible elastic rods. Phys Lett A, 2000, 270(3/4): 140--148
[26] Himonas A, Misiolek G, Ponce G, Zhou Y. Persistence properties and unique continuation of solutions of the Camassa-Holm equation. Comm Math Phys, 2007, 271(2): 511--522
[27] Constantin A. Finite propagation speed for the Camassa-Holm equation. J Math Phys, 2005, 46(023506): 1--4
[28] Benjamin T B, Bona J L, Mahony J J. Model equations for long waves in nonlinear dispersive systems. Philos Trans Roy Soc London, Ser A, 1972, 272(1220): 47--78
[29] Kato T. Quasi-linear Equations of Evolution, with Applications to Partial Differential Equations. Spectral Theory and Differential Equations. Berlin: Springer, 1975: 25--70
[30] Zhou Y. Local well-posedness and blow-up criteria of solutions for a rod equation. {Math Nachr}, 2005, 278(14): 1726--1739
[31] Zhou Y. Stability of solitary waves for a rod equation. Chaos Solitons \& Fractals, 2004, 21(4): 977--981
[32] Grillakis M, Shatah J, Strauss W. Stability theory of solitary waves in the presence of symmetry. I J Funct Anal, 1987, 74(1): 160--197
[33] Guo Z, Zhou Y. Wave breaking and persistence properties for the dispersive rod equation. SIAM J Math Anal, 2009, 40(6): 2567--2580
[34] Liu Y. 准地转运动稳定性的数学方法. 华东师范大学学报(自然科学版), 2008, 1: 1--19
[35] Liu Y, Zhou Y. Blow-up phenomenon for a periodic rod equation. J Phys A, 2008, 41: 34401
[36] Zhou Y. Blow-up of solutions to a nonlinear dispersive rod equation. Calc Var Partial Differential Equations, 2005, 25(1): 63--77 |