The geodesic hypothesis and non-topological solitons on pseudo-riemannian manifolds

David M. A. Stuart

Annales scientifiques de l'École Normale Supérieure (2004)

  • Volume: 37, Issue: 2, page 312-362
  • ISSN: 0012-9593

How to cite

top

Stuart, David M. A.. "The geodesic hypothesis and non-topological solitons on pseudo-riemannian manifolds." Annales scientifiques de l'École Normale Supérieure 37.2 (2004): 312-362. <http://eudml.org/doc/82633>.

@article{Stuart2004,
author = {Stuart, David M. A.},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {semi-linear wave equation; non-topological solitons; geodesics},
language = {eng},
number = {2},
pages = {312-362},
publisher = {Elsevier},
title = {The geodesic hypothesis and non-topological solitons on pseudo-riemannian manifolds},
url = {http://eudml.org/doc/82633},
volume = {37},
year = {2004},
}

TY - JOUR
AU - Stuart, David M. A.
TI - The geodesic hypothesis and non-topological solitons on pseudo-riemannian manifolds
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2004
PB - Elsevier
VL - 37
IS - 2
SP - 312
EP - 362
LA - eng
KW - semi-linear wave equation; non-topological solitons; geodesics
UR - http://eudml.org/doc/82633
ER -

References

top
  1. [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. [2] Berestycki H., Lions P.-L., Nonlinear scalar field equations. I. Existence of a ground state, Arch. Rat. Mech. Anal.82 (1983) 313-345. Zbl0533.35029MR695535
  3. [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. Zbl0522.35036
  4. [4] Bronski J., Jerrard R., Soliton dynamics in a potential, Math. Res. Lett.7 (2000) 329-342. Zbl0955.35067MR1764326
  5. [5] Coffman C.V., Uniqueness of the ground state solution for Δu−u+u3=0 and a variational characterization of other solutions, Arch. Rat. Mech. Anal.46 (1972) 81-95. Zbl0249.35029
  6. [6] Folland G.B., Introduction to Partial Differential Equations, Princeton University Press, Princeton, NJ, 1995. Zbl0841.35001MR1357411
  7. [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. Zbl0656.35122MR901236
  8. [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. Zbl0711.58013MR1081647
  9. [9] Keraani S., Semiclassical limit of a class of Schrödinger equations with potential, Comm. Partial Differential Equations27 (2002) 693-704. Zbl0998.35052MR1900559
  10. [10] Lee T.D., Particle Physics and Introduction to Field Theory, Harwood, Chur, 1984. 
  11. [11] Manasse F., Misner C., Fermi normal coordinates and some basic concepts in differential geometry, J. Math. Physics4 (1963) 735-745. Zbl0118.22903MR155665
  12. [12] Marsden J., Lectures on Mechanics, LMS Lecture Note Series, vol. 174, LMS, Cambridge, 1992. Zbl0744.70004MR1171218
  13. [13] Mcleod K., Uniqueness of positive radial solutions of Δu+f(u)=0 in Rn, Trans. Amer. Math. Soc.339 (1993) 495-505. Zbl0804.35034
  14. [14] Misner C.W., Thorne K.S., Wheeler J.A., Gravitation, Freeman, San Francisco, 1973. MR418833
  15. [15] Peletier L., Serrin J., Uniqueness of positive solutions of semilinear equations in Rn, Arch. Rat. Mech. Anal.81 (2) (1983) 181-197. Zbl0516.35031MR682268
  16. [16] Shatah J., Stable standing waves of nonlinear Klein–Gordon equations, Comm. Math. Phys.91 (1983) 313-327. Zbl0539.35067MR723756
  17. [17] Shatah J., Strauss W., Instability of nonlinear bound states, Comm. Math. Phys.100 (1985) 173-190. Zbl0603.35007MR804458
  18. [18] Strauss W., Existence of solitary waves in higher dimensions, Comm. Math. Phys.55 (1977) 149-162. Zbl0356.35028MR454365
  19. [19] Strauss W., Nonlinear Wave Equations, AMS, Providence, RI, 1989. Zbl0714.35003MR1032250
  20. [20] Stuart D., Solitons on pseudo-Riemannian manifolds I, Comm. PDE1815–1838 (1998) 149-191. Zbl0935.35143MR1641729
  21. [21] Stuart D.M.A., Geodesics and the Einstein nonlinear wave system, University of Cambridge preprint. Zbl1072.58021MR2059135
  22. [22] Stuart D.M.A., Solitons on pseudo-Riemannian manifolds: stability and motion, Electron. Res. Announc. Amer. Math. Soc.6 (2000) 75-89. Zbl0959.58038MR1783091
  23. [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. Zbl1158.35389MR1810509
  24. [24] Stuart D.M.A., Geodesics and the Einstein-nonlinear wave system, C. R. Acad. Sci. Paris Ser. I336 (2003) 615-618. Zbl1038.35139MR1981480
  25. [25] Tataru D., Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients II, Amer. J. Math.123 (3) (2001) 385-423. Zbl0988.35037MR1833146
  26. [26] Weinberg S., Gravitation and Cosmology, Wiley, New York, 1972. 
  27. [27] Weinstein M.I., Nonlinear Schrödinger equations and sharp interpolation estimates, Comm. Math. Phys.87 (4) (1983) 567-576. Zbl0527.35023MR691044
  28. [28] Weinstein M.I., Modulational stability of ground states of nonlinear Schrödinger equations, SIAM J. Math. Anal.16 (1985) 472-491. Zbl0583.35028MR783974

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.