On peut définir l'indice de Maslov pour une onde solitaire en approchant l'onde solitaire par des ondes périodiques : lorsqu'une suite d'ondes périodiques converge vers l'onde solitaire ϕ, alors sa limite peut-être utilisée comme définition de l'indice de Maslov de ϕ.
A Maslov index for a solitary wave can be defined by approximating the solitary wave with periodic waves: when a sequence of periodic waves converges to the solitary wave ϕ, then the sequence of Maslov indices converges and its limit can be used as a definition for the Maslov index of ϕ.
Accepté le :
Publié le :
@article{CRMATH_2007__345_12_689_0, author = {Chardard, Fr\'ed\'eric}, title = {Maslov index for solitary waves obtained as a limit of the {Maslov} index for periodic waves}, journal = {Comptes Rendus. Math\'ematique}, pages = {689--694}, publisher = {Elsevier}, volume = {345}, number = {12}, year = {2007}, doi = {10.1016/j.crma.2007.11.003}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2007.11.003/} }
TY - JOUR AU - Chardard, Frédéric TI - Maslov index for solitary waves obtained as a limit of the Maslov index for periodic waves JO - Comptes Rendus. Mathématique PY - 2007 SP - 689 EP - 694 VL - 345 IS - 12 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2007.11.003/ DO - 10.1016/j.crma.2007.11.003 LA - en ID - CRMATH_2007__345_12_689_0 ER -
%0 Journal Article %A Chardard, Frédéric %T Maslov index for solitary waves obtained as a limit of the Maslov index for periodic waves %J Comptes Rendus. Mathématique %D 2007 %P 689-694 %V 345 %N 12 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2007.11.003/ %R 10.1016/j.crma.2007.11.003 %G en %F CRMATH_2007__345_12_689_0
Chardard, Frédéric. Maslov index for solitary waves obtained as a limit of the Maslov index for periodic waves. Comptes Rendus. Mathématique, Tome 345 (2007) no. 12, pp. 689-694. doi : 10.1016/j.crma.2007.11.003. http://archive.numdam.org/articles/10.1016/j.crma.2007.11.003/
[1] A topological invariant arising in the stability analysis of traveling waves, J. Reine Angew. Math., Volume 410 (1990), pp. 167-272
[2] Characteristic class entering in quantization conditions, Funktsional. Anal. i Prilozhen., Volume 1 (1967) no. 1, pp. 1-14
[3] Stability of the in-phase travelling wave solution in a pair of coupled nerve fibers, Indiana Univ. Math. J., Volume 44 (1995) no. 1, pp. 189-220
[4] F. Chardard, F. Dias, T.J. Bridges, Computing the Maslov index of solitary waves, in preparation
[5] Fast computation of the Maslov Index for hyperbolic linear systems with periodic coefficients, J. Phys. A: Math. Gen., Volume 39 (2006) no. 47, pp. 14545-14557
[6] Count of eigenvalues in the generalized eigenvalue problem, 2006 (preprint, arXiv: pp. 1–30) | arXiv
[7] Spectral analysis of long wavelength periodic waves and applications, J. Reine Angew. Math., Volume 491 (1997), pp. 149-181
[8] Instability of standing waves for non-linear Schrödinger-type equations, Ergodic Theory Dynam. Systems, Volume 8* (1988), pp. 119-138
Cité par Sources :