References
- Arnold , VI . 1966 . Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l’hydrodynamique des fluides parfaits . Ann. Inst. Fourier (Grenoble) , 16 : 319 – 361 .
- Arnold , VI and Khesin , BA . 1998 . Topological Methods in Hydrodynamics , New York : Springer-Verlag .
- Camassa , R and Holm , DD . 1993 . An integrable shallow water equation with peaked solitons . Phys. Rev. Lett. , 71 : 1661 – 1664 .
- Camassa , R , Holm , DD and Hyman , J . 1994 . A new integrable shallow water equation . Adv. Appl. Mech. , 31 : 1 – 33 .
- Constantin , A . 1997 . On the Cauchy problem for the periodic Camassa-Holm equation . J. Differen-tial Equations , 141 : 218 – 235 .
- Constantin , A . 2001 . A Lagrangian approximation to the water-wave problem . Applied Mathematics Letters , 14 : 789 – 795 .
- Constantin , A and Escher , J . 1998 . Well-posedness global existence and blow-up phenomena for a periodic quasi-linear hyperbolic equation . Comm. Pure Appl. Math. , 51 : 475 – 504 .
- Constantin , A and Escher , J . 1998 . Wave breaking for nonlinear nonlocal shallow water equations . Acta Mathematica , 181 : 229 – 243 .
- Constantin , A and Escher , J . 2000 . On the blow-up rate and the blow-up set of breaking waves for a shallow water equation . Math. Z. , 233 : 75 – 91 .
- Constantin , A and Kolev , B . 2001 . Least action principle for an integrable shallow water equation . J. Nonlinear Math. Phys. , 8 : 471 – 474 .
- Constantin , A and Kolev , B . 2002 . On the geometric approach to the motion of inertial mechanical systems . J. Phys. A , 35 : R51 – R79 .
- Constantin , A and Kolev , B . 2003 . Geodesic flow on the diffeomorphism group of the circle . Comment. Math. Helv. , 78 : 787 – 804 .
- Constantin , A and McKean , HP . 1999 . A shallow water equation on the circle . Comm. Pure Appl. Math. , 52 : 949 – 982 .
- Cushman , R and van der , Kallen W . 2003 . Adjoint and coadjoint orbits of the Poincaré group . ArXiv , math.RT/0305442
- Ebin , DG and Marsden , J . 1970 . Groups of diffeomorphisms and the motion of an incompressible fluid . Ann. of Math. , 92 : 102 – 163 .
- Fokas , AS and Fuchssteiner , B . 1981 . Symplectic structures, their Bäcklund transformations and hereditary symmetries . Phys. D , 4 : 47 – 66 .
- Hamilton , RS . 1982 . The inverse function theorem of Nash and Moser . Bull. Amer. Math. Soc. (N.S.) , 7 : 65 – 222 .
- Hörmander , L . 1997 . Lectures on Nonlinear Hyperbolic Differential Equations , Berlin : Springer-Verlag .
- Johnson , RS and Camassa-Holm . 2002 . Korteweg-de Vries and related models for water waves . J. Fluid Mech. , 455 : 63 – 82 .
- Lang , S . 1999 . Fundamentals of Differential Geometry , New York : Springer-Verlag .
- Lax , PD . 1968 . Integrals of nonlinear equations of evolution and solitary waves . Comm. Pure Appl. Math. , 21 : 467 – 490 .
- Marsden , JE and Ratiu , TS . 1999 . Introduction to mechanics and symmetry , New York : Springer-Verlag .