@article{AIHPC_2006__23_6_849_0, author = {Martel, Yvan and Merle, Frank}, title = {Multi solitary waves for nonlinear {Schr\"odinger} equations}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {849--864}, publisher = {Elsevier}, volume = {23}, number = {6}, year = {2006}, doi = {10.1016/j.anihpc.2006.01.001}, mrnumber = {2271697}, zbl = {05138722}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2006.01.001/} }
TY - JOUR AU - Martel, Yvan AU - Merle, Frank TI - Multi solitary waves for nonlinear Schrödinger equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2006 SP - 849 EP - 864 VL - 23 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2006.01.001/ DO - 10.1016/j.anihpc.2006.01.001 LA - en ID - AIHPC_2006__23_6_849_0 ER -
%0 Journal Article %A Martel, Yvan %A Merle, Frank %T Multi solitary waves for nonlinear Schrödinger equations %J Annales de l'I.H.P. Analyse non linéaire %D 2006 %P 849-864 %V 23 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2006.01.001/ %R 10.1016/j.anihpc.2006.01.001 %G en %F AIHPC_2006__23_6_849_0
Martel, Yvan; Merle, Frank. Multi solitary waves for nonlinear Schrödinger equations. Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) no. 6, pp. 849-864. doi : 10.1016/j.anihpc.2006.01.001. http://www.numdam.org/articles/10.1016/j.anihpc.2006.01.001/
[1] Nonlinear scalar field equations. I. Existence of a ground state, Arch. Rational Mech. Anal. 82 (1983) 313-345. | MR | Zbl
, ,[2] Orbital stability of standing waves for some nonlinear Schrödinger equations, Comm. Math. Phys. 85 (1982) 549-561. | MR | Zbl
, ,[3] The Cauchy problem for the critical nonlinear Schrödinger equation in , Nonlinear Anal. 14 (1990) 807-836. | MR | Zbl
, ,[4] Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979) 209-243. | MR | Zbl
, , ,[5] On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case, J. Funct. Anal. 32 (1979) 1-32. | MR | Zbl
, ,[6] Uniqueness of positive solutions of in , Arch. Rational Mech. Anal. 105 (1989) 243-266. | MR | Zbl
,[7] Existence of nonstationary bubbles in higher dimension, J. Math. Pures Appl. 81 (2002) 1207-1239. | MR | Zbl
,[8] Asymptotic N-soliton-like solutions of the generalized critical and subcritical Korteweg-de Vries equations, Amer. J. Math. 127 (2005) 1103-1140. | MR | Zbl
,[9] Asymptotic stability of solitons for subcritical gKdV equations revisited, Nonlinearity 18 (2005) 55-80. | MR | Zbl
, ,[10] Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations, Comm. Math. Phys. 231 (2002) 347-373. | MR | Zbl
, , ,[11] Y. Martel, F. Merle, T.-P. Tsai, Stability in of the sum of K solitary waves for some nonlinear Schrödinger equations in one and two space dimensions, Duke Math. J., in press. | MR | Zbl
[12] Uniqueness of positive radial solutions of in . II, Trans. Amer. Math. Soc. 339 (1993) 495-505. | MR | Zbl
,[13] Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity, Comm. Math. Phys. 129 (1990) 223-240. | MR | Zbl
,[14] -solutions for nonlinear Schrödinger equations and nonlinear group, Funkcial. Ekvac. 30 (1987) 115-125. | MR | Zbl
,[15] Modulational stability of ground states of nonlinear Schrödinger equations, SIAM J. Math. Anal. 16 (1985) 472-491. | MR | Zbl
,[16] Lyapunov stability of ground states of nonlinear dispersive evolution equations, Comm. Pure Appl. Math. 39 (1986) 51-68. | MR | Zbl
,[17] Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Sov. Phys. JETP 34 (1972) 62-69. | MR
, ,Cité par Sources :