A Class of Equations with Peakon and Pulson Solutions (with an Appendix by Harry Braden and John Byatt-Smith)

References

• Aczél J. Lectures on functional equations and their applications, Academic Press, New York 1966
   Google Scholar
• Beals R. Sattinger D. Szmigielski J. Multipeakons and the classical moment problem, Adv. Math. 154 (2000), 229–257
   Google Scholar
• Beals R. Sattinger D. Szmigielski J. Multi-peakons and a theorem of Stieltjes, Inverse Problems 15 (1999) L1-L4
   Google Scholar
• Beals R. Sattinger D. Szmigielski J. Peakon-antipeakon interaction, J. Nonlinear Math. Phys. 8 (2001) Suppl. 23–27
   Google Scholar
• Braden H.W. Byatt-Smith J.G.B. On a Functional Differential Equation of Determinantal Type, Bull. Lond. Math. Soc. 31 (1999), 463–470
   Google Scholar
• Camassa R. Holm D.D. An integrable shallow water equation with peaked solitons, Phys. Rev. Lett. 71 (1993), 1661–1664
   Google Scholar
• Camassa R. Holm D.D. Hyman J.M. A New Integrable Shallow Water Equation, Advances in Applied Mechanics 31 (1994), 1–33
   Google Scholar
• Calogero F. Classical many-body problems amenable to exact treatments, Lecture Notes in Physics Monograph 66, Springer–Verlag (2001)
   Google Scholar
• Calogero F. Francoise J.-P. A completely integrable Hamiltonian system, J. Math. Phys. 37 (1996), 2863–2871
   Google Scholar
• Constantin A. McKean H. P. A shallow water equation on the circle , Comm. Pure Appl. Math. 52 (1999), 949–982
   Google Scholar
• Constantin A. Molinet L. Global weak solutions for a shallow water equation, Comm. Math. Phys. 211 (2000), 45–61
   Google Scholar
• Constantin A. On the scattering problem for the Camassa-Holm equation, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 457 (2001), 953–970
   Google Scholar
• Constantin A. Strauss W. Stability of peakons, Comm. Pure Appl. Math. 53 (2000), 603–610
   Google Scholar
• Constantin A. Molinet L. Orbital stability of solitary waves for a shallow water equation, Physica D 157 (2001), 75–89
   Google Scholar
• Constantin A. Kolev B. On the geometric approach to the motion of inertial mechanical systems, J. Phys. A 35 (2002) R51-R79
   Google Scholar
• Constantin A. Kolev B. Geodesic flow on the diffeomorphism group of the circle, Comment. Math. Helv. 78 (2003), 787–804
   Google Scholar
• Degasperis A. Procesi M. Asymptotic integrability, in Symmetry and Perturbation Theory (eds. A. Degasperis and G. Gaeta), World Scientific (1999), 23–37
   Google Scholar
• Degasperis A. Hone A.N.W. Holm D.D. A New Integrable Equation with Peakon Solutions, Theoret. Math. Phys. 133 (2002), 1461–1472
   Google Scholar
• Degasperis A. Hone A.N.W. Holm D.D. Integrable and non-integrable equations with peakons, in Nonlinear Physics: Theory and Experiment II, eds. M.J. Ablowitz, M. Boiti, F. Pempinelli & B. Prinari, World Scientific (2003) 37–43; nlin.SI/0209008
   Google Scholar
• Dullin H.R. Gottwald G.A. Holm D.D. Camassa-Holm, Korteweg–de Vries-5 and other asymptotically equivalent equations for shallow water, Fluid Dynamics Research 33 (2003), 73–95
   Google Scholar
• Dullin H.R. Gottwald G.A. Holm D.D. On asymptotically equivalent shallow water wave equations, Physica D 190 (2004), 1–14
   Google Scholar
• Fringer O. Holm D.D. Integrable vs. nonintegrable geodesic soliton behaviour, Physica D 150 (2001), 237–263
   Google Scholar
• Fuchssteiner B. Fokas A.S. Symplectic structures, their Bäcklund transformations, and hereditary symmetries, Physica D 4 (1981) 47
   Google Scholar
• Holm D.D. Staley M.F. Wave Structures and Nonlinear Balances in a Family of 1+1 Evolutionary PDEs, SIAM J. Appl. Dyn. Syst. 2 (2003), 323–380
   Google Scholar
• Holm D.D. Hone A.N.W. Nonintegrability of a fifth order equation with integrable two-body dynamics, Theoret. Math. Phys. 137 (2003), 1459–1471
   Google Scholar
• Holm D.D. Marsden J.E. Momentum Maps and Measure-valued Solutions (Peakons, Filaments and Sheets) for the EPDiff Equation, nlin.CD/0312048
   Google Scholar
• Hone A.N.W. The associated Camassa-Holm equation and the KdV equation, J. Phys. A 32 (1999) L307–L314
   Google Scholar
• Hone A.N.W. Reciprocal link for 2+1-dimensional Extensions of Shallow Water Equations, Applied Mathematics Letters 13 (2000), 37–42
   Google Scholar
• Hone A.N.W. Jing Ping Wang Prolongation algebras and Hamiltonian operators for peakon equations, Inverse Problems 19 (2003), 129–145
   Google Scholar
• Hone A.N.W. Painlevé tests, singularity structure and integrability, in What is Integrability?, ed. A.V. Mikhailov, Princeton University Press, to appear; preprint (2003) UKC/IMS/03/33
   Google Scholar
• Johnson R. S. Camassa-Holm, Korteweg-de Vries and related models for water waves, J. Fluid Mech. 455 (2002), 63–82
   Google Scholar
• Kraenkel R.A. Zenchuk A. Two-dimensional integrable generalization of the Camassa-Holm equation Phys. Lett. A 260 (1999), 218–224
   Google Scholar
• Mikhailov A.V. Novikov V.S. Perturbative symmetry approach, J. Phys. A 35 (2002), 4775–4790
   Google Scholar
• Misiolek G. A shallow water equation as a geodesic flow on the Bott-Virasoro group, J. Geom. Phys. 24 (1998), 203–208
   Google Scholar
• Olver P.J. Applications of Lie Groups to Differential Equations, 2nd edition, Springer-Verlag (1993)
   Google Scholar
• Olver P.J. Rosenau P. Tri-Hamiltonian Duality Between Solitons and Compactons, Phys. Rev. E 53 (1996), 1900–1906
   Google Scholar
• Parkes E.J. Vakhnenko V.O. The calculation of multi-soltion solutions of the Vakhnenko equation by the inverse scattering method, Chaos, Solitons and Fractals 13 (2002), 1819–1826
   Google Scholar
• Vakhnenko V.O. Solitons in a nonlinear model medium, J. Phys. A 25 (1992), 4181–4187
   Google Scholar