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Bennewitz, C.; Brown, Brian Malcolm; Weikard, R.
Languages: English
Types: Unknown
Subjects: QA75

Classified by OpenAIRE into

arxiv: Nonlinear Sciences::Exactly Solvable and Integrable Systems, Physics::Fluid Dynamics
We present a spectral and inverse spectral theory for the zero\ud dispersion spectral problem associated with the Camassa-Holm equation.\ud This is an alternative approach to that in [10] by Eckhardt and\ud Teschl.
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    • [1] Christer Bennewitz. Spectral asymptotics for Sturm-Liouville equations. Proc. London Math. Soc. (3), 59(2):294{338, 1989.
    • [2] C. Bennewitz, B. M. Brown, and R. Weikard. Inverse spectral and scattering theory for the half-line left-de nite Sturm-Liouville problem. SIAM J. Math. Anal., 40(5):2105{2131, 2009.
    • [3] Bennewitz, C., Brown, B. M. and Weikard, R. Scattering and inverse scattering for a left-de nite Sturm-Liouville problem. J. Di erential Equations 253 (2012), no. 8, 2380{2419.
    • [4] Louis de Branges Hilbert spaces of entire functions Prentice-Hall, Englewood Cli s, 1968.
    • [5] Camassa, Roberto and Holm, Darryl D. An integrable shallow water equation with peaked solitons. Phys. Rev. Lett. 71 (1993), no. 11, 1661{1664.
    • [6] A. Constantin and H. P. McKean, A shallow water equation on the circle, Comm. Pure Appl. Math., 52 (1999), pp. 949{982.
    • [7] Constantin, A. On the scattering problem for the Camassa-Holm equation. R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 457 (2001), pp. 953{970.
    • [8] Adrian Constantin. Existence of permanent and breaking waves for a shallow water equation: a geometric approach. Ann. Inst. Fourier (Grenoble), 50(2):321{ 362, 2000.
    • [9] Adrian Constantin and Joachim Escher. Wave breaking for nonlinear nonlocal shallow water equations. Acta Math., 181(2):229{243, 1998.
    • [10] Eckhardt, Jonathan and Teschl, Gerald. On the isospectral problem of the dispersionless Camassa-Holm equation. Adv. Math. 235 (2013), 469{495.
    • [11] Eckhardt, Jonathan. Direct and inverse spectral theory of singular left-de nite Sturm-Liouville operators. J. Di erential Equations 253 (2012), no. 2, 604634.
    • [12] B. Fuchssteiner and A. S. Fokas. Symplectic structures, their Backlund transformations and hereditary symmetries. Phys. D, 4(1):47{66, 1981/82.
    • [13] Koliander, G. Hilbert Spaces of Entire Functions in the Hardy Space Setting. Diplomarbeit, Technische Universitat Wien, 2011.
    • [14] B. Ja. Levin. Distribution of zeros of entire functions, volume 5 of Translations of Mathematical Monographs. American Mathematical Society, Providence, R.I., revised edition, 1980. Translated from the Russian by R. P. Boas, J. M. Danskin, F. M. Goodspeed, J. Korevaar, A. L. Shields and H. P. Thielman.
    • [15] Z. Jiang, L. Ni, and Y. Zhou. Wave breaking of the Camassa-Holm equation, J. Nonlinear Sci., 22(2): 235{245, 2012.
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