Multi solitary waves for nonlinear Schrödinger equations

Martel, Yvan; Merle, Frank

doi:10.1016/j.anihpc.2006.01.001

Martel, Yvan ; Merle, Frank

Annales de l'I.H.P. Analyse non linéaire, Tome 23 (2006) no. 6, pp. 849-864.

MR Zbl | 4 citations dans Numdam

DOI : 10.1016/j.anihpc.2006.01.001

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     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://archive.numdam.org/articles/10.1016/j.anihpc.2006.01.001/}
}

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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://archive.numdam.org/articles/10.1016/j.anihpc.2006.01.001/

Bibliographie
Cité par

[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 | Zbl

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

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

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

[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 | Zbl

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

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

[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 | Zbl

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

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

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

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

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

[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

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