The geodesic hypothesis and non-topological solitons on pseudo-riemannian manifolds
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 37 (2004) no. 2, p. 312-362
@article{ASENS_2004_4_37_2_312_0,
     author = {Stuart, David M. A.},
     title = {The geodesic hypothesis and non-topological solitons on pseudo-riemannian manifolds},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Elsevier},
     volume = {Ser. 4, 37},
     number = {2},
     year = {2004},
     pages = {312-362},
     doi = {10.1016/j.ansens.2003.07.001},
     zbl = {1054.58026},
     mrnumber = {2061784},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_2004_4_37_2_312_0}
}
Stuart, David M. A. The geodesic hypothesis and non-topological solitons on pseudo-riemannian manifolds. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 37 (2004) no. 2, pp. 312-362. doi : 10.1016/j.ansens.2003.07.001. http://www.numdam.org/item/ASENS_2004_4_37_2_312_0/

[1] Anderson D.L.T., Stability of time-dependent particle-like solutions in nonlinear field theories, II, J. Math. Phys. 12 (1971) 945-952.

[2] Berestycki H., Lions P.-L., Nonlinear scalar field equations. I. Existence of a ground state, Arch. Rat. Mech. Anal. 82 (1983) 313-345. | MR 695535 | Zbl 0533.35029

[3] Berestycki H., Lions P.-L., Peletier L., An ODE approach to existence of positive solutions for semilinear problems in Rn, Indiana Univ. Math. J. 30 (1983) 141-157. | Zbl 0522.35036

[4] Bronski J., Jerrard R., Soliton dynamics in a potential, Math. Res. Lett. 7 (2000) 329-342. | MR 1764326 | Zbl 0955.35067

[5] Coffman C.V., Uniqueness of the ground state solution for Δuu+u3=0 and a variational characterization of other solutions, Arch. Rat. Mech. Anal. 46 (1972) 81-95. | Zbl 0249.35029

[6] Folland G.B., Introduction to Partial Differential Equations, Princeton University Press, Princeton, NJ, 1995. | MR 1357411 | Zbl 0841.35001

[7] Grillakis M., Shatah J., Strauss W., Stability theory of solitary waves in the presence of symmetry, I, J. Funct. Anal. 74 (1987) 160-197. | MR 901236 | Zbl 0656.35122

[8] Grillakis M., Shatah J., Strauss W., Stability theory of solitary waves in the presence of symmetry, II, J. Funct. Anal. 94 (1990) 308-348. | MR 1081647 | Zbl 0711.58013

[9] Keraani S., Semiclassical limit of a class of Schrödinger equations with potential, Comm. Partial Differential Equations 27 (2002) 693-704. | MR 1900559 | Zbl 0998.35052

[10] Lee T.D., Particle Physics and Introduction to Field Theory, Harwood, Chur, 1984.

[11] Manasse F., Misner C., Fermi normal coordinates and some basic concepts in differential geometry, J. Math. Physics 4 (1963) 735-745. | MR 155665 | Zbl 0118.22903

[12] Marsden J., Lectures on Mechanics, LMS Lecture Note Series, vol. 174, LMS, Cambridge, 1992. | MR 1171218 | Zbl 0744.70004

[13] Mcleod K., Uniqueness of positive radial solutions of Δu+f(u)=0 in Rn, Trans. Amer. Math. Soc. 339 (1993) 495-505. | Zbl 0804.35034

[14] Misner C.W., Thorne K.S., Wheeler J.A., Gravitation, Freeman, San Francisco, 1973. | MR 418833

[15] Peletier L., Serrin J., Uniqueness of positive solutions of semilinear equations in Rn, Arch. Rat. Mech. Anal. 81 (2) (1983) 181-197. | MR 682268 | Zbl 0516.35031

[16] Shatah J., Stable standing waves of nonlinear Klein-Gordon equations, Comm. Math. Phys. 91 (1983) 313-327. | MR 723756 | Zbl 0539.35067

[17] Shatah J., Strauss W., Instability of nonlinear bound states, Comm. Math. Phys. 100 (1985) 173-190. | MR 804458 | Zbl 0603.35007

[18] Strauss W., Existence of solitary waves in higher dimensions, Comm. Math. Phys. 55 (1977) 149-162. | MR 454365 | Zbl 0356.35028

[19] Strauss W., Nonlinear Wave Equations, AMS, Providence, RI, 1989. | MR 1032250 | Zbl 0714.35003

[20] Stuart D., Solitons on pseudo-Riemannian manifolds I, Comm. PDE 1815-1838 (1998) 149-191. | MR 1641729 | Zbl 0935.35143

[21] Stuart D.M.A., Geodesics and the Einstein nonlinear wave system, University of Cambridge preprint. | MR 2059135

[22] Stuart D.M.A., Solitons on pseudo-Riemannian manifolds: stability and motion, Electron. Res. Announc. Amer. Math. Soc. 6 (2000) 75-89. | MR 1783091 | Zbl 0959.58038

[23] Stuart D.M.A., Modulational approach to stability of non-topological solitons in semilinear wave equations, J. Math. Pures Appl. 80 (1) (2001) 51-83. | MR 1810509 | Zbl 01595997

[24] Stuart D.M.A., Geodesics and the Einstein-nonlinear wave system, C. R. Acad. Sci. Paris Ser. I 336 (2003) 615-618. | MR 1981480 | Zbl 1038.35139

[25] Tataru D., Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients II, Amer. J. Math. 123 (3) (2001) 385-423. | MR 1833146 | Zbl 0988.35037

[26] Weinberg S., Gravitation and Cosmology, Wiley, New York, 1972.

[27] Weinstein M.I., Nonlinear Schrödinger equations and sharp interpolation estimates, Comm. Math. Phys. 87 (4) (1983) 567-576. | MR 691044 | Zbl 0527.35023

[28] Weinstein M.I., Modulational stability of ground states of nonlinear Schrödinger equations, SIAM J. Math. Anal. 16 (1985) 472-491. | MR 783974 | Zbl 0583.35028