[1] Alarcon E A, Iorio R J. The existence of global attractors for a class of nonlinear dissipative evolution equations. Proceedings of the Royal Society of Edinburgh Section A:Mathematics, 2005, 135(5):887-913
[2] Babin A V, Vishik M I. Attractors of Evolution Equations//Attractors of evolution equations. NorthHolland, 1992
[3] de Monvel A B, Shepelsky D. Riemann-Hilbert approach for the Camassa-Holm equation on the line. Comptes Rendus Mathematique, 2006, 343(10):627-632
[4] Beals R, Sattinger D H, Szmigielski J. Multi-peakons and a theorem of Stieltjes. Inverse Problems, 1999, 15(1):L1-L4
[5] Constantin A, McKean H P. A shallow water equation on the circle. Communications on Pure and Applied Mathematics, 1999, 52(8):949-982
[6] Camassa R, Holm D D. An integrable shallow water equation with peaked solitons. Physical Review Letters, 1993, 71(11):1661-1664
[7] Camassa R, Holm D D, Hyman J M. A new integrable shallow water equation. Advances in Applied Mechanics, 1994, 31:1-33
[8] Chen R M, Liu Y. Wave breaking and global existence for a generalized two-component Camassa-Holm system. International Mathematics Research Notices, 2010, 2011(6):1381-1416
[9] Chen M, Zhang Y. A two-component generalization of the Camassa-Holm equation and its solutions. Letters in Mathematical Physics, 2006, 75(1):1-15
[10] Constantin A, Strauss W A. Stability of peakons. Communications on Pure and Applied Mathematics, 2000, 53(5):603-610
[11] Constantin A, Strauss W A. Stability of a class of solitary waves in compressible elastic rods. Physics Letters A, 2000, 270(3):140-148
[12] Constantin A. On the scattering problem for the Camassa-Holm equation//Proceedings of the Royal Society of London A:Mathematical, Physical and Engineering Sciences. The Royal Society, 2001, 457(2008):953-970
[13] Constantin A. On the inverse spectral problem for the Camassa-Holm equation. Journal of Functional Analysis, 1998, 155(2):352-363
[14] Constantin A, Gerdjikov V S, Ivanov R I. Inverse scattering transform for the Camassa-Holm equation. Inverse Problems, 2006, 22(6):2197-2207
[15] Ding D, Tian L. The attractor in dissipative Camassa-Holm equation. Acta Mathematicae Applicatae Sinica, 2004, 27(3):536-545
[16] Dai H H. Model equations for nonlinear dispersive waves in a compressible Mooney-Rivlin rod. Acta Mechanica, 1998, 127(1/4):193-207
[17] Escher J, Lechtenfeld O, Yin Z. Well-posedness and blow-up phenomena for the 2-component CamassaHolm equation. Discrete and continuous dynamical systems, 2007, 19(3):493-513
[18] Falqui G. On a Camassa-Holm type equation with two dependent variables. Journal of Physics A:Mathematical and General, 2005, 39(2):327-342
[19] Fuchssteiner B, Fokas A S. Symplectic structures, their Bäcklund transformations and hereditary symmetries. Physica D:Nonlinear Phenomena, 1981, 4(1):47-66
[20] Wei F, Da-Jun Z. The Hamiltonian structures of μ-equations related to periodic peakons. Chinese Physics Letters, 2013, 30(8):080201
[21] Fuchssteiner B. Some tricks from the symmetry-toolbox for nonlinear equations:generalizations of the Camassa-Holm equation. Physica D:Nonlinear Phenomena, 1996, 95(3/4):229-243
[22] Guan C, Yin Z. Global existence and blow-up phenomena for an integrable two-component Camassa-Holm shallow water system. Journal of Differential Equations, 2010, 248(8):2003-2014
[23] Gui G, Liu Y. On the global existence and wave-breaking criteria for the two-component Camassa-Holm system. Journal of Functional Analysis, 2010, 258(12):4251-4278
[24] Gui G, Liu Y. On the Cauchy problem for the two-component Camassa-Holm system. Mathematische Zeitschrift, 2011, 268(1):45-66
[25] Gui G, Liu Y, Zhu M. On the wave-breaking phenomena and global existence for the generalized periodic Camassa-Holm equation. International Mathematics Research Notices, 2011, 2012(21):4858-4903
[26] Guo F, Gao H, Liu Y. On the wave-breaking phenomena for the two-component Dullin-Gottwald-Holm system. Journal of the London Mathematical Society, 2012, 86(3):810-834
[27] Gurevich A V, Zybin K P, Gnedin N Y, et al. Nondissipative gravitational turbulence. Zh Eksp Teor Fiz, 1988, 94:3-25
[28] Hunter J K, Saxton R. Dynamics of director fields. SIAM Journal on Applied Mathematics, 1991, 51(6):1498-1521
[29] Hunter J K, Zheng Y. On a completely integrable nonlinear hyperbolic variational equation. Physica D:Nonlinear Phenomena, 1994, 79(2/4):361-386
[30] Ito M. Symmetries and conservation laws of a coupled nonlinear wave equation. Physics Letters A, 1982, 91(7):335-338
[31] Ivanov R. Two-component integrable systems modelling shallow water waves:the constant vorticity case. Wave Motion, 2009, 46(6):389-396
[32] Johnson R S. Camassa-Holm, Korteweg-de Vries and related models for water waves. Journal of Fluid Mechanics, 2002, 455:63-82
[33] Kolev B. Poisson brackets in Hydrodynamics. Discrete and Continuous Dynamical Systems-Series A, 2007, 19(3):555-574
[34] Khesin B, Lenells J, Misio lek G. Generalized Hunter-Saxton equation and the geometry of the group of circle diffeomorphisms. Mathematische Annalen, 2008, 342(3):617-656
[35] Liu J, Yin Z. On the Cauchy problem of a periodic 2-component μ-Hunter-Saxton system. Nonlinear Analysis:Theory, Methods & Applications, 2012, 75(1):131-142
[36] Liu J. The Cauchy problem of a periodic 2-component μ-Hunter-Saxton system in Besov spaces. Journal of Mathematical Analysis and Applications, 2013, 399(2):650-666
[37] Liu J, Yin Z. Global weak solutions for a periodic two-component μ-Hunter-Saxton system. Monatshefte für Mathematik, 2012, 168(3/4):503-521
[38] Lenells J, Misio lek G, Tiǧlay F. Integrable evolution equations on spaces of tensor densities and their peakon solutions. Communications in Mathematical Physics, 2010, 299(1):129-161
[39] Lenells J. Conservation laws of the Camassa-Holm equation. Journal of Physics A:Mathematical and General, 2005, 38(4):869-880
[40] Olver P J, Rosenau P. Tri-Hamiltonian duality between solitons and solitary-wave solutions having compact support. Physical Review E, 1996, 53(2):1900-1906
[41] Tian L, Fan J. The attractor on viscosity Degasperis-Procesi equation. Nonlinear Analysis:Real World Applications, 2008, 9(4):1461-1473
[42] Tian L, Gao Y. The global attractor of the viscous Fornberg-Whitham equation. Nonlinear Analysis:Theory, Methods & Applications, 2009, 71(11):5176-5186
[43] Tian L, Tian R. The attractor for the two-dimensional weakly damped KdV equation in belt field. Nonlinear Analysis:Real World Applications, 2008, 9(3):912-919
[44] Tian L, Xu Y, Zhou J. Attractor for the viscous two-component Camassa-Holm equation. Nonlinear Analysis:Real World Applications, 2012, 13(3):1115-1129
[45] Tian L, Xu Y. Attractor for a viscous coupled Camassa-Holm equation. Advances in Difference Equations, 2010, 2010(1):512812
[46] Temam R. Infinite-dimensional dynamical systems in mechanics and physics. Springer Science & Business Media, 2012
[47] Wang F, Li F, Chen Q. Wave breaking and global existence for a weakly dissipative generalized twocomponent μ-Hunter-Saxton system. Nonlinear Analysis:Real World Applications, 2015, 23:61-77
[48] Yin Z. On the Structure of Solutions to the Periodic Hunter-Saxton Equation. SIAM Journal on Mathematical Analysis, 2004, 36(1):272-283
[49] Zuo D. A two-component μ-Hunter-Saxton equation. Inverse Problems, 2010, 26(8):085003
[50] Zong X, Sun S. On the global attractor of the two-component π-Camassa-Holm equation with viscous terms. Nonlinear Analysis:Real World Applications, 2014, 20:82-98
[51] Zheng S. Nonlinear evolution equations. CRC Press, 2004
