@article{ASNSP_1998_4_26_2_303_0,
author = {Constantin, Adrian and Escher, Joachim},
title = {Global existence and blow-up for a shallow water equation},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {303--328},
year = {1998},
publisher = {Scuola normale superiore},
volume = {Ser. 4, 26},
number = {2},
mrnumber = {1631589},
zbl = {0918.35005},
language = {en},
url = {https://www.numdam.org/item/ASNSP_1998_4_26_2_303_0/}
}
TY - JOUR AU - Constantin, Adrian AU - Escher, Joachim TI - Global existence and blow-up for a shallow water equation JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 1998 SP - 303 EP - 328 VL - 26 IS - 2 PB - Scuola normale superiore UR - https://www.numdam.org/item/ASNSP_1998_4_26_2_303_0/ LA - en ID - ASNSP_1998_4_26_2_303_0 ER -
%0 Journal Article %A Constantin, Adrian %A Escher, Joachim %T Global existence and blow-up for a shallow water equation %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 1998 %P 303-328 %V 26 %N 2 %I Scuola normale superiore %U https://www.numdam.org/item/ASNSP_1998_4_26_2_303_0/ %G en %F ASNSP_1998_4_26_2_303_0
Constantin, Adrian; Escher, Joachim. Global existence and blow-up for a shallow water equation. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 26 (1998) no. 2, pp. 303-328. https://www.numdam.org/item/ASNSP_1998_4_26_2_303_0/
[1] - - - , On the link between umbilic geodesics and soliton solutions of nonlinear PDE's, Proc. Roy. Soc. London, Ser. A 450 (1995), 677-692. | Zbl | MR
[2] - - - , The geometry of peaked solitons and billiard solutions of a class of integrable PDE's, Lett. Math. Phys. 32 (1994), 137-151. | Zbl | MR
[3] - - , Model equations for long waves in nonlinear dispersive systems, Philos. Trans. Roy. Soc. London, Ser. A 272 (1972), 47-78. | Zbl | MR
[4] - - , Solitary wave interaction, Phys. Fluids 23 (1980), 438-441. | Zbl
[5] , Fourier restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations II, Geom. Funct. Anal. 3 (1993), 209-262. | Zbl | MR
[6] , An integrable Hamiltonian system, Phys. Lett. A 201 (1995), 306-310. | Zbl | MR
[7] - , A completely integrable Hamiltonian system, J. Math. Phys. 37 (1996), 2863-2871. | Zbl | MR
[8] - , Solvable quantum version of an integrable Hamiltonian system, J. Math. Phys. 37 (1996), 4243-4251. | Zbl | MR
[9] - , An integrable shallow water equation with peaked solitons, Phys. Rev. Lett. 71 (1993), 1661-1664. | Zbl | MR
[10] - - , A new integrable shallow water equation, Adv. Appl. Mech. 31 (1994), 1-33. | Zbl
[11] , The Hamiltonian structure of the Camassa-Holm equation, Expositiones Math. 15 (1997), 53-85. | Zbl | MR
[12] , On the Cauchy problem for the periodic Camassa-Holm equation, J. Differential Equations 141 (1997), 218-235. | Zbl | MR
[13] - , Well-posedness and existence of global solutions for a periodic quasi-linear hyperbolic equation, Comm. Pure Appl. Math. 51 (1998), 475-504. | Zbl | MR
[14] - , Solitons in the Camassa-Holm shallow water equation, Phys. Lett. A 194 (1994), 246-250. | Zbl | MR
[15] - - - , Solitons and Nonlinear Wave Equations, Academic Press, New York, 1984. | Zbl | MR
[16] - , Symplectic structures, their Bäcklund transformation and hereditary symmetries, Phys. D 4 (1981), 47-66. | MR
[17] , Some tricks from the symmetry-toolbox for nonlinear equations: generalizations of the Camassa-Holm equation, Phys. D 95 (1996), 296-343. | Zbl | MR
[18] - , Elliptic Partial Differential Equations of Second Order, Springer Verlag, Berlin, 1977. | Zbl | MR
[19] , Quasi-linear equations of evolution, with applications to partial differential equations, In: "Spectral Theory and Differential Equations ", 448, Springer Lecture Notes in Mathematics, 1975, pp. 25-70. | Zbl | MR
[20] , On the Cauchy problem for the (generalized) Korteweg-de Vries equation, Stud. Appl. Math. 8 (1983), 93-126. | Zbl | MR
[21] , Integrals of nonlinear equations of evolution and solitary waves, Comm. Pure Appl. Math. 21 (1968), 467-490. | Zbl | MR
[22] , Integrable systems and algebraic curves, In: "Global Analysis ", 755, Springer Lecture Notes in Mathematics, 1979, pp. 83-200. | Zbl | MR
[23] - , Nonlinear Nonlocal Equations in the Theory of Waves, vol. 133, Transl. Math. Monographs, Providence, Rhode Island, 1994. | Zbl | MR
[24] , Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, New York, 1983. | Zbl | MR
[25] , Zero curvature formulations of dual hierarchies, J. Math. Phys. 37 (1996), 1928-1938. | Zbl | MR
[26] , Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, 1993. | Zbl | MR
[27] , Linear and Nonlinear Waves, J. Wiley & Sons, New York, 1980. | MR






