On construit des solutions au problème de la propagation de deux ondes solitaires avec distance logarithmique de Schrödinger non linéaire,
Dans le cas intégrable ( et ), l'existence d'une telle solution est connue par la méthode dite d'inverse scaterring (E. Olmedilla, Multiple pole solutions of the nonlinear Schrödinger equation, Physica D 25 (1987) 330–346 ; T. Zakharov, A.B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Sov. Phys. JETP 34 (1972) 62–69). Le cas d'une masse critique introduit un comportement spécifique lié à l'explosion, qui a été étudié précédemment par Y. Martel et P. Raphaël (Strongly interacting blow up bubbles for the mass critical NLS, Ann. Sci. Éc. Norm. Supér. 51 (2018) 701–737).
We construct 2-solitary wave solutions with logarithmic distance to the nonlinear Schrödinger equation,
In the integrable case ( and ), the existence of such solutions is known by inverse scattering (E. Olmedilla, Multiple pole solutions of the nonlinear Schrödinger equation, Physica D 25 (1987) 330–346; T. Zakharov, A.B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Sov. Phys. JETP 34 (1972) 62–69). The mass-critical case exhibits a specific behavior related to blow-up, previously studied in Y. Martel, P. Raphaël (Strongly interacting blow up bubbles for the mass critical NLS, Ann. Sci. Éc. Norm. Supér. 51 (2018) 701–737).
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Tiến Vinh Nguyễn 1
@article{CRMATH_2019__357_1_13_0, author = {Tiến Vinh Nguyễn}, title = {Existence of multi-solitary waves with logarithmic relative distances for the {NLS} equation}, journal = {Comptes Rendus. Math\'ematique}, pages = {13--58}, publisher = {Elsevier}, volume = {357}, number = {1}, year = {2019}, doi = {10.1016/j.crma.2018.11.012}, language = {en}, }
Tiến Vinh Nguyễn. Existence of multi-solitary waves with logarithmic relative distances for the NLS equation. Comptes Rendus. Mathématique, Volume 357 (2019) no. 1, pp. 13-58. doi : 10.1016/j.crma.2018.11.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.11.012/
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