Multipeakons and the classical moment problem

Advances in Mathematics

Volumn 154, Issue 2, 2000, Pages 229-257

  Beals, Richard ^a   Sattinger, David H ^b   Szmigielski, Jacek ^c  

^a YALE UNIVERSITY   (United States)

^b UTAH STATE UNIVERSITY   (United States)

^c UNIVERSITY OF SASKATCHEWAN   (Canada)

Author keywords

Collisions; Continued fractions; Multipeakons; Scattering

Indexed keywords

EID: 0034714658     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.1999.1883     Document Type: Article

References (24)

1. N. I. Akhiezer, "The classical moment problem," University Mathematical Monographs, Oliver & Boyd, Edinburgh/London, 1965.
2. M. S. Alber, R. Camassa, D. D. Holm, and J. E. Marsden, The geometry of peaked solitons & billiard solutions of a class of integrable PDE's, Letts. Math. Phys. 32 (1994), 137-151.
3. M. S. Alber, R. Camassa, D. D. Holm, and J. E. Marsden, On the link between umbilic geodesics & soliton solutions of nonlinear PDEs, Proc. Roy. Soc. London Ser. A 450 (1995), 677-692.
4. V. Barcilon, Inverse problem for the vibrating beam in the free-clamped configuration, Philos. Trans. Roy. Soc. London Ser. A 304 (1982), 211-251.
5. R. Beals, D. H. Sattinger, and J. Szmigielski, Acoustic scattering and the extended Korteweg-deVries hierarchy, Adv. Math. 140 (1998), 190-206.
6. R. Beals, D. H. Sattinger, and J. Szmigielski, Multipeakons and a theorem of Stieltjes, Inverse Problems 15 (1999), L1-L4.
7. R. Camassa and D. D. Holm, An integrable shallow water equation with peaked solitons, Phys. Rev. Lett. 71 (1993), 1661-1664.
8. R. Camassa, D. D. Holm, and J. M. Hyman, A new integrable shallow water equation, Adv. Appl. Mech. 31 (1994), 1-33.
9. A. Constantin and J. Escher, Global existence and blow-up for a shallow water equation, Ann. Scuola Sup. Pisa 26 (1998), 303-328.
10. A. Constantin and J. Escher, Wave breaking for nonlinear nonlocal shallow water equations, Acta Math. 181 (1998), 229-243.
11. G. Frobenius, Über relationen zwischen der Näherungsbruchen von Potenzreihen, J. Reine Angew. Math. 90 (1881), 1-17.
12. B. Fuchssteiner, The lie algebra structure of nonlinear evolution equations admitting infinite dimensional Abelian symmetry groups, Progr. Theoret. Phys. 65 (1981), 861-876.
13. A. E. Green and P. M. Naghdi, A derivation of equations for wave propagation in water of variable depth, J. Fluid Mech. 78 (1976), 237-246.
14. M. G. Krein, Determination of the density of an inhomogeneous symmetric string from its frequency spectrum, Dokl. Akad. Nauk SSSR 76 (1951), 345-348.
15. M. G. Krein, On inverse problems for an inhomogeneous string, Dokl. Akad. Nauk SSSR 82 (1952), 669-672.
16. H. P. McKean, Singular Curves and the Toda Lattice, preprint, Courant Institute of Mathematical Sciences, New York.
17. H. P. McKean, Breakdown of a Shallow Water Equation, preprint, Courant Institute of Mathematical Sciences, New York, 1998.
18. J. Moser, Finitely many mass points on the line under the influence of an exponential potential - An integrable systems, in "Dynamical Systems, Theory and Applications," Lecture Notes in Phys., Vol. 38, pp. 467-497, Springer-Verlag, Berlin, 1975.
19. J. Moser, Three integrable Hamiltonian systems connected with isospectral deformations, Adv. Math. 16 (1975), 197-220.
20. P. Rosenau, Nonlinear dispersion and compact structures, Phys. Rev. Lett. 73 (1994), 1737-1741.
21. B. Simon, A new approach to inverse spectral theory. I. Fundamental formalism, Ann. Math., in press.
22. T. J. Stieltjes, Recherches sur les fractions continues, in "Oeuvres Complètes de Thomas Jan Stieltjes," Vol. II, pp. 402-566, Nordhoff, Groningen, 1918.
23. G. G. Stokes, "On the Theory of Oscillatory Waves," Vol. I, pp. 197-229, Cambridge Univ. Press, Cambridge, UK, 1880.
24. G. B. Whitham, "Linear and Nonlinear Waves," Wiley, New York, 1973.