Multi solitary waves for nonlinear Schrödinger equations

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1. [1] Berestycki H., Lions P.-L., Nonlinear scalar field equations. I. Existence of a ground state, Arch. Rational Mech. Anal.82 (1983) 313-345. Zbl0533.35029MR695535
2. [2] Cazenave T., Lions P.L., Orbital stability of standing waves for some nonlinear Schrödinger equations, Comm. Math. Phys.85 (1982) 549-561. Zbl0513.35007MR677997
3. [3] Cazenave T., Weissler F., The Cauchy problem for the critical nonlinear Schrödinger equation in $H^s$, Nonlinear Anal.14 (1990) 807-836. Zbl0706.35127MR1055532
4. [4] Gidas B., Ni W.M., Nirenberg L., Symmetry and related properties via the maximum principle, Comm. Math. Phys.68 (1979) 209-243. Zbl0425.35020MR544879
5. [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. Zbl0396.35028MR533218
6. [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. Zbl0676.35032MR969899
7. [7] Mariş M., Existence of nonstationary bubbles in higher dimension, J. Math. Pures Appl.81 (2002) 1207-1239. Zbl1040.35116MR1952162
8. [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. Zbl1090.35158MR2170139
9. [9] Martel Y., Merle F., Asymptotic stability of solitons for subcritical gKdV equations revisited, Nonlinearity18 (2005) 55-80. Zbl1064.35171MR2109467
10. [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. Zbl1017.35098MR1946336
11. [11] Y. Martel, F. Merle, T.-P. Tsai, Stability in $H^1$ of the sum ofK solitary waves for some nonlinear Schrödinger equations in one and two space dimensions, Duke Math. J., in press. Zbl1099.35134MR2228459
12. [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. Zbl0804.35034MR1201323
13. [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. Zbl0707.35021MR1048692
14. [14] Tsutsumi Y., $L^2$-solutions for nonlinear Schrödinger equations and nonlinear group, Funkcial. Ekvac.30 (1987) 115-125. Zbl0638.35021MR915266
15. [15] Weinstein M.I., Modulational stability of ground states of nonlinear Schrödinger equations, SIAM J. Math. Anal.16 (1985) 472-491. Zbl0583.35028MR783974
16. [16] Weinstein M.I., Lyapunov stability of ground states of nonlinear dispersive evolution equations, Comm. Pure Appl. Math.39 (1986) 51-68. Zbl0594.35005MR820338
17. [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. JETP34 (1972) 62-69. MR406174