Spikes in two coupled nonlinear Schrödinger equations
Annales de l'I.H.P. Analyse non linéaire (2005)
- Volume: 22, Issue: 4, page 403-439
- ISSN: 0294-1449
Access Full Article
topHow to cite
topLin, Tai-Chia, and Wei, Juncheng. "Spikes in two coupled nonlinear Schrödinger equations." Annales de l'I.H.P. Analyse non linéaire 22.4 (2005): 403-439. <http://eudml.org/doc/78662>.
@article{Lin2005,
author = {Lin, Tai-Chia, Wei, Juncheng},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Hartree-Fock theory; Fermi gas; Nehari's manifold; least-energy solution; Bose-Einstein condensates},
language = {eng},
number = {4},
pages = {403-439},
publisher = {Elsevier},
title = {Spikes in two coupled nonlinear Schrödinger equations},
url = {http://eudml.org/doc/78662},
volume = {22},
year = {2005},
}
TY - JOUR
AU - Lin, Tai-Chia
AU - Wei, Juncheng
TI - Spikes in two coupled nonlinear Schrödinger equations
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2005
PB - Elsevier
VL - 22
IS - 4
SP - 403
EP - 439
LA - eng
KW - Hartree-Fock theory; Fermi gas; Nehari's manifold; least-energy solution; Bose-Einstein condensates
UR - http://eudml.org/doc/78662
ER -
References
top- [1] Bates P., Fusco G., Equilibria with many nuclei for the Cahn–Hilliard equation, J. Differential Equations160 (2000) 283-356. Zbl0990.35016MR1737000
- [2] Bates P., Dancer E.N., Shi J., Multi-spike stationary solutions of the Cahn–Hilliard equation in higher-dimension and instability, Adv. Differential Equations4 (1999) 1-69. Zbl1157.35407MR1667283
- [3] Conti M., Terracini S., Verzini G., Nehari's problem and competing species system, Ann. Inst. H. Poincaré19 (6) (2002) 871-888. Zbl1090.35076MR1939088
- [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. Zbl0932.35080MR1736974
- [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. Zbl0942.35058MR1742305
- [6] del Pino M., Felmer P., Wei J., On the role of distance function in some singularly perturbed problems, Comm. Partial Differential Equations25 (2000) 155-177. Zbl0949.35054MR1737546
- [7] del Pino M., Felmer P., Wei J., Multiple peak solutions for some singular perturbation problems, Cal. Var. Partial Differential Equations10 (2000) 119-134. Zbl0974.35041MR1750734
- [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, Nature19 (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 Equations157 (1999) 82-101. Zbl1087.35507MR1710015
- [10] Dancer E.N., Yan S., Multipeak solutions for a singular perturbed Neumann problem, Pacific J. Math.189 (1999) 241-262. Zbl0933.35070MR1696122
- [11] Estaban M.J., Lions P.L., Existence and non-existence results for semilinear problems in unbounded domains, Proc. Roy. Soc. Edinburgh Sect. A93 (1982) 1-14. Zbl0506.35035MR688279
- [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 , in: Mathematical Analysis and Applications, Part A, Adv. Math. Suppl. Stud., vol. 7A, Academic Press, New York, 1981, pp. 369-402. Zbl0469.35052MR634248
- [14] Gui C., Wei J., Multiple interior spike solutions for some singular perturbed Neumann problems, J. Differential Equations158 (1999) 1-27. Zbl1061.35502MR1721719
- [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. Zbl0949.35052MR1758231
- [16] Gui C., Wei J., Winter M., Multiple boundary peak solutions for some singularly perturbed Neumann problems, Ann. Inst. H. Poincaré Anal. Non Linéaire17 (2000) 249-289. Zbl0944.35020MR1743431
- [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 Equations11 (2000) 143-175. Zbl0964.35047MR1782991
- [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, Science300 (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 in , Arch. Rational Mech. Anal.105 (1989) 243-266. Zbl0676.35032MR969899
- [21] Li Y.-Y., On a singularly perturbed equation with Neumann boundary condition, Comm. Partial Differential Equations23 (1998) 487-545. Zbl0898.35004MR1620632
- [22] Li Y.-Y., Nirenberg L., The Dirichlet problem for singularly perturbed elliptic equations, Comm. Pure Appl. Math.51 (1998) 1445-1490. Zbl0933.35083MR1639159
- [23] Lieband E., Loss M., Analysis, American Mathematical Society, 1996. Zbl0873.26002
- [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. Zbl0917.35047MR1490535
- [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. Zbl0754.35042MR1115095
- [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. Zbl0796.35056MR1219814
- [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. Zbl0838.35009MR1342381
- [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 Equations42 (3) (1981) 400-413. Zbl0486.35032MR639230
- [31] Wei J., On the construction of single-peaked solutions to a singularly perturbed semilinear Dirichlet problem, J. Differential Equations129 (1996) 315-333. Zbl0865.35011MR1404386
- [32] Wei J., On the interior spike layer solutions to a singularly perturbed Neumann problem, Tohoku Math. J.50 (1998) 159-178. Zbl0918.35024MR1622042
- [33] Wei J., On the effect of the domain geometry in a singularly perturbed Dirichlet problem, Differential Integral Equations13 (2000) 15-45. Zbl0970.35034MR1811947
- [34] Wei J., On the boundary spike layer solutions of singularly perturbed semilinear Neumann problem, J. Differential Equations134 (1997) 104-133. Zbl0873.35007MR1429093
- [35] Wei J., Winter M., Stationary solutions for the Cahn–Hilliard equation, Ann. Inst. H. Poincaré Anal. Non Linéaire15 (1998) 459-492. Zbl0910.35049MR1632937
- [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. Zbl0922.35025MR1709667
Citations in EuDML Documents
topNotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.