Spikes in two coupled nonlinear Schrödinger equations
Annales de l'I.H.P. Analyse non linéaire, Volume 22 (2005) no. 4, p. 403-439
@article{AIHPC_2005__22_4_403_0,
author = {Lin, Tai-Chia and Wei, Juncheng},
title = {Spikes in two coupled nonlinear Schr\"odinger equations},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {22},
number = {4},
year = {2005},
pages = {403-439},
doi = {10.1016/j.anihpc.2004.03.004},
zbl = {1080.35143},
mrnumber = {2145720},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2005__22_4_403_0}
}

Lin, Tai-Chia; Wei, Juncheng. Spikes in two coupled nonlinear Schrödinger equations. Annales de l'I.H.P. Analyse non linéaire, Volume 22 (2005) no. 4, pp. 403-439. doi : 10.1016/j.anihpc.2004.03.004. http://www.numdam.org/item/AIHPC_2005__22_4_403_0/

[1] Bates P., Fusco G., Equilibria with many nuclei for the Cahn-Hilliard equation, J. Differential Equations 160 (2000) 283-356. | MR 1737000 | Zbl 0990.35016

[2] Bates P., Dancer E.N., Shi J., Multi-spike stationary solutions of the Cahn-Hilliard equation in higher-dimension and instability, Adv. Differential Equations 4 (1999) 1-69. | MR 1667283 | Zbl 01493588

[3] Conti M., Terracini S., Verzini G., Nehari's problem and competing species system, Ann. Inst. H. Poincaré 19 (6) (2002) 871-888. | Numdam | MR 1939088 | Zbl 1090.35076

[4] Del Pino M., Felmer P., Spike-layered solutions of singularly perturbed elliptic problems in a degenerate setting, Indiana Univ. Math. J. 48 (3) (1999) 883-898. | MR 1736974 | Zbl 0932.35080

[5] Del Pino M., Felmer P., Wei J., On the role of mean curvature in some singularly perturbed Neumann problems, SIAM J. Math. Anal. 31 (1999) 63-79. | MR 1742305 | Zbl 0942.35058

[6] Del Pino M., Felmer P., Wei J., On the role of distance function in some singularly perturbed problems, Comm. Partial Differential Equations 25 (2000) 155-177. | MR 1737546 | Zbl 0949.35054

[7] Del Pino M., Felmer P., Wei J., Multiple peak solutions for some singular perturbation problems, Cal. Var. Partial Differential Equations 10 (2000) 119-134. | MR 1750734 | Zbl 0974.35041

[8] Donley E.A., Claussen N.R., Cornish S.L., Roberts J.L., Cornell E.A., Wieman C.E., Dynamics of collapsing and exploding Bose-Einstein condensates, Nature 19 (412) (2001) 295-299.

[9] Dancer E.N., Wei J., On the location of spike s of solutions with two sharp layers for a singularly perturbed semilinear Dirichlet problem, J. Differential Equations 157 (1999) 82-101. | MR 1710015 | Zbl 1087.35507

[10] Dancer E.N., Yan S., Multipeak solutions for a singular perturbed Neumann problem, Pacific J. Math. 189 (1999) 241-262. | MR 1696122 | Zbl 0933.35070

[11] Estaban M.J., Lions P.L., Existence and non-existence results for semilinear problems in unbounded domains, Proc. Roy. Soc. Edinburgh Sect. A 93 (1982) 1-14. | MR 688279 | Zbl 0506.35035

[12] Esry B.D., Greene C.H., Burke J.P., Bohn J.L., Hartree-Fock theory for double condensates, Phys. Rev. Lett. 78 (1997) 3594-3597.

[13] Gidas B., Ni W.-M., Nirenberg L., Symmetry of positive solutions of nonlinear elliptic equations in ${R}^{n}$, in: Mathematical Analysis and Applications, Part A, Adv. Math. Suppl. Stud., vol. 7A, Academic Press, New York, 1981, pp. 369-402. | MR 634248 | Zbl 0469.35052

[14] Gui C., Wei J., Multiple interior spike solutions for some singular perturbed Neumann problems, J. Differential Equations 158 (1999) 1-27. | MR 1721719 | Zbl 1061.35502

[15] Gui C., Wei J., On multiple mixed interior and boundary peak solutions for some singularly perturbed Neumann problems, Canad. J. Math. 52 (2000) 522-538. | MR 1758231 | Zbl 0949.35052

[16] Gui C., Wei J., Winter M., Multiple boundary peak solutions for some singularly perturbed Neumann problems, Ann. Inst. H. Poincaré Anal. Non Linéaire 17 (2000) 249-289. | Numdam | MR 1743431 | Zbl 0944.35020

[17] Grossi M., Pistoia A., Wei J., Existence of multipeak solutions for a semilinear Neumann problem via nonsmooth critical point theory, Cal. Var. Partial Differential Equations 11 (2000) 143-175. | MR 1782991 | Zbl 0964.35047

[18] Gupta S., Hadzibabic Z., Zwierlein M.W., Stan C.A., Dieckmann K., Schunck C.H., Van Kempen E.G.M., Verhaar B.J., Ketterle W., Radio-frequency spectroscopy of ultracold fermions, Science 300 (2003) 1723-1726.

[19] Hall D.S., Matthews M.R., Ensher J.R., Wieman C.E., Cornell E.A., Dynamics of component separation in a binary mixture of Bose-Einstein condensates, Phys. Rev. Lett. 81 (1998) 1539-1542.

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

[21] Li Y.-Y., On a singularly perturbed equation with Neumann boundary condition, Comm. Partial Differential Equations 23 (1998) 487-545. | MR 1620632 | Zbl 0898.35004

[22] Li Y.-Y., Nirenberg L., The Dirichlet problem for singularly perturbed elliptic equations, Comm. Pure Appl. Math. 51 (1998) 1445-1490. | MR 1639159 | Zbl 0933.35083

[23] Lieband E., Loss M., Analysis, American Mathematical Society, 1996. | Zbl 0873.26002

[24] Myatt C.J., Burt E.A., Ghrist R.W., Cornell E.A., Wieman C.E., Production of two overlapping Bose-Einstein condensates by sympathetic cooling, Phys. Rev. Lett. 78 (1997) 586-589.

[25] Ni W.-M., Diffusion, cross-diffusion, and their spike-layer steady states, Notices Amer. Math. Soc. 45 (1998) 9-18. | MR 1490535 | Zbl 0917.35047

[26] Ni W.-M., Takagi I., On the shape of least energy solution to a semilinear Neumann problem, Comm. Pure Appl. Math. 41 (1991) 819-851. | MR 1115095 | Zbl 0754.35042

[27] Ni W.-M., Takagi I., Locating the peaks of least energy solutions to a semilinear Neumann problem, Duke Math. J. 70 (1993) 247-281. | MR 1219814 | Zbl 0796.35056

[28] Ni W.-M., Wei J., On the location and profile of spike-Layer solutions to singularly perturbed semilinear Dirichlet problems, Comm. Pure Appl. Math. 48 (1995) 731-768. | MR 1342381 | Zbl 0838.35009

[29] Timmermans E., Phase separation of Bose-Einstein condensates, Phys. Rev. Lett. 81 (1998) 5718-5721.

[30] Troy W., Symmetry properties in systems of semilinear elliptic equations, J. Differential Equations 42 (3) (1981) 400-413. | MR 639230 | Zbl 0486.35032

[31] Wei J., On the construction of single-peaked solutions to a singularly perturbed semilinear Dirichlet problem, J. Differential Equations 129 (1996) 315-333. | MR 1404386 | Zbl 0865.35011

[32] Wei J., On the interior spike layer solutions to a singularly perturbed Neumann problem, Tohoku Math. J. 50 (1998) 159-178. | MR 1622042 | Zbl 0918.35024

[33] Wei J., On the effect of the domain geometry in a singularly perturbed Dirichlet problem, Differential Integral Equations 13 (2000) 15-45. | MR 1811947 | Zbl 0970.35034

[34] Wei J., On the boundary spike layer solutions of singularly perturbed semilinear Neumann problem, J. Differential Equations 134 (1997) 104-133. | MR 1429093 | Zbl 0873.35007

[35] Wei J., Winter M., Stationary solutions for the Cahn-Hilliard equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 15 (1998) 459-492. | Numdam | MR 1632937 | Zbl 0910.35049

[36] Wei J., Winter M., Multiple boundary spike solutions for a wide class of singular perturbation problems, J. London Math. Soc. 59 (1999) 585-606. | MR 1709667 | Zbl 0922.35025