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Existence and orbital stability of standing waves for nonlinear Schrödinger systems. (English) Zbl 06618019

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
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[1] Albert, J.; Bhattarai, S., Existence and stability of a two-parameter family of solitary waves for an NLS-KdV system, Adv. Differential Equations, 18, 1129-1164, (2013) · Zbl 1290.35219
[2] Bagnato, V. S.; Frantzeskakis, D. J.; Kevrekidis, P. G.; Malomed, B. A.; Mihalache, D., Bose-Einstein condensation: twenty years after, Romanian Rep. Phys., 67, 5-50, (2015)
[3] T. Bartsch, L. Jeanjean, Normalized solutions for nonlinear Schrödinger systems, Proc. Edinb. Math. Soc. ArXiv identifier arXiv:1507.04649. · Zbl 1393.35035
[4] Bellazzini, J.; Siciliano, G., Scaling properties of functionals and existence of constrained minimizers, J. Funct. Anal., 261, 2486-2507, (2011) · Zbl 1357.49053
[5] Bhattarai, S., Stability of normalized solitary waves for three coupled nonlinear Schrödinger equations, Discrete Contin. Dyn. Syst. Ser. A, 36, 1789-1811, (2016) · Zbl 1326.35331
[6] Byeon, J., Effect of symmetry to the structure of positive solutions in nonlinear elliptic problems, J. Differential Equations, 163, 429-474, (2000) · Zbl 0952.35054
[7] Cao, D.; Chern, I.-L.; Wei, J., On ground state of spinor Bose-Einstein condensates, NoDEA Nonlinear Differential Equations Appl., 18, 427-445, (2011) · Zbl 1228.35218
[8] Cazenave, T.; Lions, P.-L., Orbital stability of standing waves for some nonlinear Schrödinger equations, Comm. Math. Phys., 85, 549-561, (1982) · Zbl 0513.35007
[9] Chen, Z.; Zou, W., Existence and symmetry of positive ground states for a doubly critical Schrödinger system, Trans. Amer. Math. Soc., 367, 3599-3646, (2015) · Zbl 1315.35091
[10] Cipolatti, R.; Zumpichiatti, W., Orbital stable standing waves for a system of coupled nonlinear Schrödinger equations, Nonlinear Anal., 42, 445-461, (2000) · Zbl 0964.35147
[11] Colin, M.; Jeanjean, L.; Squassina, M., Stability and instability results for standing waves of quasi-linear Schrödinger equations, Nonlinearity, 23, 1353-1385, (2010) · Zbl 1192.35163
[12] Esry, B. D.; Greene, C. H.; Burke, J. P.; Bohn, J. L., Hartree-Fock theory for double condensates, Phys. Rev. Lett., 78, 3594-3597, (1997)
[13] Garrisi, D., On the orbital stability of standing-wave solutions to a coupled nonlinear Klein-Gordon equation, Adv. Nonlinear Stud., 12, 639-658, (2012) · Zbl 1269.35039
[14] Hajaiej, H., Symmetric ground states solutions of m-coupled nonlinear Schrödinger equation, Nonlinear Anal. TMA, 71, 4696-4704, (2009) · Zbl 1167.35513
[15] Ikoma, N., Existence of minimizers for some coupled nonlinear Schrödinger equations, (Geometric Properties for Parabolic and Elliptic PDE’s, Vol. 2, (2013)), 143-164 · Zbl 1291.35350
[16] Ikoma, N., Compactness of minimizing sequences in nonlinear Schrödinger systems under multiconstraint conditions, Adv. Nonlinear Stud., 14, 115-136, (2014) · Zbl 1297.35218
[17] Jeanjean, L.; Squassina, M., An approach to minimization under a constraint: the added mass technique, Calc. Var. Partial Differential Equations, 41, 511-534, (2011) · Zbl 1223.49021
[18] Lieb, E. H.; Loss, M., (Analysis, Graduate Studies in Mathematics, vol. 14, (2001), American Mathematical Society Providence)
[19] Lions, P.-L., The concentration-compactness principle in the calculus of variations. the locally compact case, part I, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1, 109-145, (1984) · Zbl 0541.49009
[20] Lions, P.-L., The concentration-compactness principle in the calculus of variations. the locally compact case, part II, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1, 223-283, (1984) · Zbl 0704.49004
[21] C. Liu, N.V. Nguyen, Z.-Q. Wang, Existence and stability of solitary waves of an M-coupled nonlinear Schrödinger system, Preprint.
[22] Malomed, B., Multi-component Bose-Einstein condensates: theory, (Kevrekidis, P. G.; Frantzeskakis, D. J.; Carretero-Gonzalez, R., Emergent Nonlinear Phenomena in Bose-Einstein Condensation, (2008), Springer-Verlag Berlin), 287-305 · Zbl 1151.82369
[23] Nguyen, N. V.; Tian, R.; Deconinck, B.; Sheils, N., Global existence of a coupled system of Schrödinger equations with power-type nonlinearities, J. Math. Phys., 54, 011503, (2013) · Zbl 1286.35230
[24] Nguyen, N. V.; Wang, Z.-Q., Orbital stability of solitary waves for a nonlinear schröinger system, Adv. Differential Equations, 16, 977-1000, (2011) · Zbl 1252.35253
[25] Nguyen, N. V.; Wang, Z.-Q., Orbital stability of solitary waves of a 3-coupled nonlinear Schrödinger system, Nonlinear Anal., 90, 1-26, (2013) · Zbl 1281.35080
[26] Nguyen, N. V.; Wang, Z.-Q., Existence and stability of a two-parameter family of solitary waves for a 2-couple nonlinear Schrödinger system, Discrete Contin. Dyn. Syst., 36, 1005-1021, (2016) · Zbl 1330.35411
[27] Ohta, M., Stability of solitary waves for coupled nonlinear Schrödinger equations, Nonlinear Anal., 26, 933-939, (1996) · Zbl 0860.35011
[28] Shibata, M., A new rearrangement inequality and its application for \(L^2\)-constraint minimizing problems, [math.AP] · Zbl 1382.35012
[29] Shibata, M., Stable standing waves of nonlinear Schrödinger equations with a general nonlinear term, Manuscripta Math., 143, 221-237, (2014) · Zbl 1290.35252
[30] Stuart, C. A., Bifurcation from the continuous spectrum in \(L^2\)-theory of elliptic equations on \(\mathbb{R}^N\), (Recent Methods in Nonlinear Analysis and Applications, (1981), Liguori Napoli)
[31] Stuart, C. A., Bifurcation for Dirichlet problems without eigenvalues, Proc. Lond. Math. Soc., 3, 45, 169-192, (1982) · Zbl 0505.35010
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