Degasperis-Procesi peakons and the discrete cubic string

International Mathematics Research Papers

Volumn 2005, Issue , 2005, Pages 53-116

  Lundmark, Hans ^a   Szmigielski, Jacek ^b  

^a LINKÖPING UNIVERSITY   (Sweden)

^b UNIVERSITY OF SASKATCHEWAN   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33845947766     PISSN: 16873017     EISSN: 16873009     Source Type: Journal    
DOI: 10.1155/imrp.2005.53     Document Type: Review

References (19)

1. A. Anderson, An elegant solution of the n-body Toda problem, J. Math. Phys. 37 (1996), no. 3, 1349-1355.
2. R. Beals, D. H. Sattinger, and J. Szmigielski, Multi-peakons and a theorem of Stieltjes, Inverse Problems 15 (1999), no. 1, L1-L4.
3. -, Multipeakons and the classical moment problem, Adv. Math. 154 (2000), no. 2, 229-257.
4. R. Camassa and D. D. Holm, An integrable shallow water equation with peaked solitons, Phys. Rev. Lett. 71 (1993), no. 11, 1661-1664.
5. A. Degasperis, D. D. Holm, and A. N. W. Hone, A new integrable equation with peakon solutions, Theoret. and Math. Phys. 133 (2002), no. 2, 1463-1474.
6. -, Integrable and non-integrable equations with peakons, Nonlinear Physics: Theory and Experiment, II (Gallipoli, 2002) (M. J. Ablowitz, M. Boiti, F. Pempinelli, and B. Prinari, eds.), World Scientific Publishing, New Jersey, 2003, pp. 37-3.
7. A. Degasperis and M. Procesi, Asymptotic integrability, Symmetry and Perturbation Theory (Rome, 1998) (A. Degasperis and G. Gaeta, eds.), World Scientific Publishing, New Jersey, 1999, pp. 23-37.
8. P. A. Deift, Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes in Mathematics, vol. 3, New York University Courant Institute of Mathematical Sciences, New York, 1999.
9. H. Dym and H. P. McKean, Gaussian Processes, Function Theory, and the Inverse Spectral Problem, Probability and Mathematical Statistics, vol. 31, Academic Press [Harcourt Brace Jovanovich Publishers], New York, 1976.
10. S. M. Fallat, M. I. Gekhtman, and C. R. Johnson, Spectral structures of irreducible totally non-negative matrices, SIAM J. Matrix Anal. Appl. 22 (2000), no. 2, 627-645.
11. S. Fomin and A. Zelevinsky, Total positivity: tests and parametrizations, Math. Intelligencer 22 (2000), no. 1,23-33.
12. F. P. Gantmacher and M. G. Krein, Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems, revised ed., AMS Chelsea Publishing, Rhode Island, 2002, translation based on the 1941 Russian original; edited and with a preface by Alex Eremenko.
13. I. S. Kac and M. G. Krein, On the spectral functions of the string, Amer. Math. Soc. Transl. Ser. 2 103 (1974), no. 2, 19-102.
14. M. Krein, Sur les fonctions de Green non-symétriques oscillatoires des opérateurs différentiels ordinaires, C. R. (Doklady) Acad. Sci. URSS (N. S.) 25 (1939), 643-646 (French).
15. H. Lundmark and J. Szmigielski, Multi-peakon solutions of the Degasperis-Procesi equation, Inverse Problems 19 (2003), no. 6, 1241-1245.
16. J. Moser, Finitely many mass points on the line under the influence of an exponential potential-an integrable system, Dynamical Systems, Theory and Applications (Rencontres, Battelle Res. Inst., Seattle, Wash, 1974), Lecture Notes in Phys., vol. 38, Springer, Berlin, 1975, pp. 467-497.
17. E. M. Nikishin and V. N. Sorokin, Rational Approximations and Orthogonality, Translations of Mathematical Monographs, vol. 92, American Mathematical Society, Rhode Island, 1991, translated from Russian by Ralph P. Boas.
18. T. J. Stieltjes, Œuvres Complètes/Collected Papers. Vol. I, II, Springer-Verlag, Berlin, 1993.
19. G. Szegö, Orthogonal Polynomials, 4th ed., American Mathematical Society Colloquium Publications, vol. 23, American Mathematical Society, Rhode Island, 1975.