Comptes Rendus
Mathematical Physics/Partial Differential Equations
Geodesics and the Einstein-nonlinear wave system
Comptes Rendus. Mathématique, Volume 336 (2003) no. 7, pp. 615-618.

Results concerning the problem of motion of test particles in the context of solitary wave solutions of the Einstein-nonlinear wave system are announced.

On étude le problème du mouvement des ondes solitaires dans le système qui comprend l'équation d'Einstein et l'équation des ondes non linéaires.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-073X(03)00126-2

David M.A. Stuart 1

1 CMS, University of Cambridge, Cambridge, CB3 OWA, UK
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David M.A. Stuart. Geodesics and the Einstein-nonlinear wave system. Comptes Rendus. Mathématique, Volume 336 (2003) no. 7, pp. 615-618. doi : 10.1016/S1631-073X(03)00126-2. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00126-2/

[1] H. Berestycki; P.L. Lions Nonlinear scalar field equations, I, Arch. Rational. Mech. Anal., Volume 82 (1983), pp. 313-345

[2] Y. Choquet-Bruhat; A. Fisher; J. Marsden Équations des contraintes sur une variété non compacte, C. R. Acad. Sci. Paris, Sér. A–B, Volume 284 (1977) no. 16, p. A975-A978

[3] M. Grillakis; W. Strauss; J. Shatah Stablility theory of solitary waves in the presence of symmetry, I, J. Funct. Anal., Volume 74 (1987), pp. 160-197

[4] T. Hughes; J. Marsden; T. Kato Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity, Arch. Rational Mech. Anal., Volume 63 (1977) no. 3, pp. 273-294

[5] K. Mcleod Uniqueness of positive radial solutions of Δu+f(u)=0 in n , Trans. Amer. Math. Soc., Volume 339 (1993), pp. 495-505

[6] D. Stuart Modulational approach to stability of non-topological solitons in semilinear wave equations, J. Math. Pures Appl., Volume 80 (2001) no. 1, pp. 51-83

[7] D. Stuart, Geodesics and the Einstein nonlinear wave system, in preparation

[8] D. Stuart, The geodesic hypothesis and non-topological solitons on pseudo-Riemannian manifolds, Preprint

[9] D. Stuart Solitons on pseudo-Riemannian manifolds: stability and motion, Electron. Res. Announc. Amer. Math. Soc., Volume 6 (2000), pp. 75-89 (electronic)

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

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