Multi solitary waves for nonlinear Schrödinger equations
Annales de l'I.H.P. Analyse non linéaire, Volume 23 (2006) no. 6, p. 849-864
@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},
publisher = {Elsevier},
volume = {23},
number = {6},
year = {2006},
pages = {849-864},
doi = {10.1016/j.anihpc.2006.01.001},
zbl = {05138722},
mrnumber = {2271697},
language = {en},
url = {http://www.numdam.org/item/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, Volume 23 (2006) no. 6, pp. 849-864. doi : 10.1016/j.anihpc.2006.01.001. http://www.numdam.org/item/AIHPC_2006__23_6_849_0/

[1] Berestycki H., Lions P.-L., Nonlinear scalar field equations. I. Existence of a ground state, Arch. Rational Mech. Anal. 82 (1983) 313-345. | MR 695535 | Zbl 0533.35029

[2] Cazenave T., Lions P.L., Orbital stability of standing waves for some nonlinear Schrödinger equations, Comm. Math. Phys. 85 (1982) 549-561. | MR 677997 | Zbl 0513.35007

[3] Cazenave T., Weissler F., The Cauchy problem for the critical nonlinear Schrödinger equation in ${H}^{s}$, Nonlinear Anal. 14 (1990) 807-836. | MR 1055532 | Zbl 0706.35127

[4] Gidas B., Ni W.M., Nirenberg L., Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979) 209-243. | MR 544879 | Zbl 0425.35020

[5] Ginibre J., Velo G., On a class of nonlinear Schrödinger equations. I. The Cauchy problem, general case, J. Funct. Anal. 32 (1979) 1-32. | MR 533218 | Zbl 0396.35028

[6] Kwong M.K., Uniqueness of positive solutions of $\Delta u+{u}^{p}=0$ in ${R}^{n}$, Arch. Rational Mech. Anal. 105 (1989) 243-266. | MR 969899 | Zbl 0676.35032

[7] Mariş M., Existence of nonstationary bubbles in higher dimension, J. Math. Pures Appl. 81 (2002) 1207-1239. | MR 1952162 | Zbl 1040.35116

[8] Martel Y., Asymptotic N-soliton-like solutions of the generalized critical and subcritical Korteweg-de Vries equations, Amer. J. Math. 127 (2005) 1103-1140. | MR 2170139 | Zbl 1090.35158

[9] Martel Y., Merle F., Asymptotic stability of solitons for subcritical gKdV equations revisited, Nonlinearity 18 (2005) 55-80. | MR 2109467 | Zbl 1064.35171

[10] Martel Y., Merle F., Tsai T.-P., 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 1946336 | Zbl 1017.35098

[11] Y. Martel, F. Merle, T.-P. Tsai, Stability in ${H}^{1}$ of the sum of K solitary waves for some nonlinear Schrödinger equations in one and two space dimensions, Duke Math. J., in press. | MR 2228459 | Zbl 1099.35134

[12] Mcleod K., Uniqueness of positive radial solutions of $\Delta u+f\left(u\right)=0$ in ${R}^{n}$. II, Trans. Amer. Math. Soc. 339 (1993) 495-505. | MR 1201323 | Zbl 0804.35034

[13] Merle F., Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity, Comm. Math. Phys. 129 (1990) 223-240. | MR 1048692 | Zbl 0707.35021

[14] Tsutsumi Y., ${L}^{2}$-solutions for nonlinear Schrödinger equations and nonlinear group, Funkcial. Ekvac. 30 (1987) 115-125. | MR 915266 | Zbl 0638.35021

[15] Weinstein M.I., Modulational stability of ground states of nonlinear Schrödinger equations, SIAM J. Math. Anal. 16 (1985) 472-491. | MR 783974 | Zbl 0583.35028

[16] Weinstein M.I., Lyapunov stability of ground states of nonlinear dispersive evolution equations, Comm. Pure Appl. Math. 39 (1986) 51-68. | MR 820338 | Zbl 0594.35005

[17] Zakharov V.E., Shabat A.B., 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 406174