Nonlinear standing and rotating waves on the sphere

[摘要] We establish the existence of time-periodic solutions of semi-linear wave equations on the unit sphere in R-3. The problem has been studied previously in (1982, V. Benci and Fortunate, Ann.. Mat. Pura Appl. 132, 215-242) using variational techniques. Our results here are much sharper: We employ delicate methods of bifurcation theory (1979, H. Kielhofer, J. Math. Anal. Appl. 68, 408-420; 1987, H. Kielhofer and P. Kotzner, J. Appl. Math. Phys. 38, 701-212) combined with well-known group-theoretic ideas to find branches of small-amplitude solutions. Precise spatio-temporal patterns of solutions are uncovered as a by-product of the analysis. Moreover, in certain cases we prove the existence of global solution branches (in the sense of P. Rabinowitz). (C) 2000 Academic Press.

[发布日期] 2000-09-20