Spikes in two coupled nonlinear Schrödinger equations

Lin, Tai-Chia; Wei, Juncheng

doi:10.1016/j.anihpc.2004.03.004

Lin, Tai-Chia ; Wei, Juncheng

Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 4, pp. 403-439.

MR Zbl | 3 citations dans Numdam

DOI : 10.1016/j.anihpc.2004.03.004

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     author = {Lin, Tai-Chia and Wei, Juncheng},
     title = {Spikes in two coupled nonlinear {Schr\"odinger} equations},
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     pages = {403--439},
     publisher = {Elsevier},
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     zbl = {1080.35143},
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Lin, Tai-Chia; Wei, Juncheng. Spikes in two coupled nonlinear Schrödinger equations. Annales de l'I.H.P. Analyse non linéaire, Tome 22 (2005) no. 4, pp. 403-439. doi : 10.1016/j.anihpc.2004.03.004. https://www.numdam.org/articles/10.1016/j.anihpc.2004.03.004/

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WANG, Chunhua; XIE, Dingyi; ZHAN, Liping; ZHANG, Lipan; ZHAO, Liangpei Segregated vector solutions for nonlinear schrödinger systems in ℝ2, Acta Mathematica Scientia, Volume 35 (2015) no. 2, p. 383 | DOI:10.1016/s0252-9602(15)60010-8
Fang, Guo-bei; Lü, Zhong-xue Existence and uniqueness of positive solutions to three coupled nonlinear Schrödinger equations, Acta Mathematicae Applicatae Sinica, English Series, Volume 31 (2015) no. 4, p. 1021 | DOI:10.1007/s10255-015-0524-y
Liu, Jiaquan; Liu, Xiangqing; Wang, Zhi-qiang Multiple mixed states of nodal solutions for nonlinear Schrödinger systems, Calculus of Variations and Partial Differential Equations, Volume 52 (2015) no. 3-4, p. 565 | DOI:10.1007/s00526-014-0724-y
Soave, Nicola On existence and phase separation of solitary waves for nonlinear Schrödinger systems modelling simultaneous cooperation and competition, Calculus of Variations and Partial Differential Equations, Volume 53 (2015) no. 3-4, p. 689 | DOI:10.1007/s00526-014-0764-3
Sato, Yohei; Wang, Zhi-Qiang Multiple positive solutions for Schrödinger systems with mixed couplings, Calculus of Variations and Partial Differential Equations, Volume 54 (2015) no. 2, p. 1373 | DOI:10.1007/s00526-015-0828-z
Byeon, Jaeyoung Semi-classical standing waves for nonlinear Schrödinger systems, Calculus of Variations and Partial Differential Equations, Volume 54 (2015) no. 2, p. 2287 | DOI:10.1007/s00526-015-0866-6
Sato, Yohei; Wang, Zhi-Qiang On the least energy sign-changing solutions for a nonlinear elliptic system, Discrete Continuous Dynamical Systems - A, Volume 35 (2015) no. 5, p. 2151 | DOI:10.3934/dcds.2015.35.2151
Pi, Huirong; Peng, Shuangjie Spike vector solutions for some coupled nonlinear Schrödinger equations, Discrete and Continuous Dynamical Systems, Volume 36 (2015) no. 4, p. 2205 | DOI:10.3934/dcds.2016.36.2205
Peng, Yanfang On elliptic systems with Sobolev critical exponent, Discrete and Continuous Dynamical Systems, Volume 36 (2015) no. 6, p. 3357 | DOI:10.3934/dcds.2016.36.3357
Yue, Xiaorui Positive ground state solutions and multiple nontrivial solutions for coupled critical elliptic systems, Journal of Mathematical Analysis and Applications, Volume 427 (2015) no. 1, p. 88 | DOI:10.1016/j.jmaa.2015.01.073
Liu, Weiming Multi-peak solutions for nonlinear Schrödinger systems with magnetic potentials inR3, Journal of Mathematical Analysis and Applications, Volume 431 (2015) no. 2, p. 1054 | DOI:10.1016/j.jmaa.2015.06.013
Zhuo, Ran; Li, FengQuan Liouville type theorems for Schrödinger systems, Science China Mathematics, Volume 58 (2015) no. 1, p. 179 | DOI:10.1007/s11425-014-4925-9
Yue, Xiaorui; Zou, Wenming A perturbation method for k-mixtures of Bose–Einstein condensates, Zeitschrift für angewandte Mathematik und Physik, Volume 66 (2015) no. 3, p. 1023 | DOI:10.1007/s00033-014-0468-8
Tang, Zhongwei Segregated peak solutions of coupled Schrödinger systems with Neumann boundary conditions, Discrete Continuous Dynamical Systems - A, Volume 34 (2014) no. 12, p. 5299 | DOI:10.3934/dcds.2014.34.5299
Long, Wei; Peng, Shuangjie Segregated vector solutions for a class of Bose–Einstein systems, Journal of Differential Equations, Volume 257 (2014) no. 1, p. 207 | DOI:10.1016/j.jde.2014.03.019
Chen, Zhijie; Lin, Chang-Shou; Zou, Wenming Monotonicity and nonexistence results to cooperative systems in the half space, Journal of Functional Analysis, Volume 266 (2014) no. 2, p. 1088 | DOI:10.1016/j.jfa.2013.08.021
Tang, Zhongwei Multi-peak solutions to coupled Schrödinger systems with Neumann boundary conditions, Journal of Mathematical Analysis and Applications, Volume 409 (2014) no. 2, p. 684 | DOI:10.1016/j.jmaa.2013.07.053
Ye, Hongyu; Peng, Yanfang Positive least energy solutions for a coupled Schrödinger system with critical exponent, Journal of Mathematical Analysis and Applications, Volume 417 (2014) no. 1, p. 308 | DOI:10.1016/j.jmaa.2014.03.028
Yin, Hui; Lü, Zhongxue Positive solutions to integral systems with weight and Bessel potentials, Journal of Mathematical Analysis and Applications, Volume 418 (2014) no. 1, p. 264 | DOI:10.1016/j.jmaa.2014.03.076
Yang, Minbo; Wei, Yuanhong; Ding, Yanheng Existence of semiclassical states for a coupled Schrödinger system with potentials and nonlocal nonlinearities, Zeitschrift für angewandte Mathematik und Physik, Volume 65 (2014) no. 1, p. 41 | DOI:10.1007/s00033-013-0317-1
Sato, Yohei; Wang, Zhi-Qiang On the multiple existence of semi-positive solutions for a nonlinear Schrödinger system, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 30 (2013) no. 1, p. 1 | DOI:10.1016/j.anihpc.2012.05.002
Peng, Shuangjie; Wang, Zhi-qiang Segregated and Synchronized Vector Solutions for Nonlinear Schrödinger Systems, Archive for Rational Mechanics and Analysis, Volume 208 (2013) no. 1, p. 305 | DOI:10.1007/s00205-012-0598-0
Zhu, Shiren; Chen, Xiaoli; Yang, Jianfu Regularity, symmetry and uniqueness of positive solutions to a nonlinear elliptic system, Communications on Pure Applied Analysis, Volume 12 (2013) no. 6, p. 2685 | DOI:10.3934/cpaa.2013.12.2685
Lei, Yutian Positive solutions of integral systems involving Bessel potentials, Communications on Pure Applied Analysis, Volume 12 (2013) no. 6, p. 2721 | DOI:10.3934/cpaa.2013.12.2721
Tian, Rushun; Wang, Zhi-Qiang Bifurcation results on positive solutions of an indefinite nonlinear elliptic system, Discrete Continuous Dynamical Systems - A, Volume 33 (2013) no. 1, p. 335 | DOI:10.3934/dcds.2013.33.335
Lin, Tai-Chia; Wu, Tsung-Fang Existence and multiplicity of positive solutions for two coupled nonlinear Schrödinger equations, Discrete Continuous Dynamical Systems - A, Volume 33 (2013) no. 7, p. 2911 | DOI:10.3934/dcds.2013.33.2911
Wang, Weichung; Wu, Tsung-Fang; Liu, Chien-Hsiang On the multiple spike solutions for singularly perturbed elliptic systems, Discrete Continuous Dynamical Systems - B, Volume 18 (2013) no. 1, p. 237 | DOI:10.3934/dcdsb.2013.18.237
Chen, Zhijie; Lin, Chang-Shou; Zou, Wenming Multiple sign-changing and semi-nodal solutions for coupled Schrödinger equations, Journal of Differential Equations, Volume 255 (2013) no. 11, p. 4289 | DOI:10.1016/j.jde.2013.08.009
Nguyen, Nghiem V.; Tian, Rushun; Deconinck, Bernard; Sheils, Natalie Global existence for a coupled system of Schrödinger equations with power-type nonlinearities, Journal of Mathematical Physics, Volume 54 (2013) no. 1 | DOI:10.1063/1.4774149
Tavares, H.; Weth, T. Existence and symmetry results for competing variational systems, Nonlinear Differential Equations and Applications NoDEA, Volume 20 (2013) no. 3, p. 715 | DOI:10.1007/s00030-012-0176-z
Essman, Michael; Shi, Junping Bifurcation diagrams of coupled Schrödinger equations, Applied Mathematics and Computation, Volume 219 (2012) no. 8, p. 3646 | DOI:10.1016/j.amc.2012.09.061
Chen, Zhijie; Zou, Wenming Positive Least Energy Solutions and Phase Separation for Coupled Schrödinger Equations with Critical Exponent, Archive for Rational Mechanics and Analysis, Volume 205 (2012) no. 2, p. 515 | DOI:10.1007/s00205-012-0513-8
Lin, Huei-li Multiple positive solutions for semilinear elliptic systems involving subcritical nonlinearities in R N, Boundary Value Problems, Volume 2012 (2012) no. 1 | DOI:10.1186/1687-2770-2012-118
Lei, Yutian; Li, Congming Integrability and asymptotics of positive solutions of a γ-Laplace system, Journal of Differential Equations, Volume 252 (2012) no. 3, p. 2739 | DOI:10.1016/j.jde.2011.10.009
Lucia, Marcello; Tang, Zhongwei Multi-bump bound states for a system of nonlinear Schrödinger equations, Journal of Differential Equations, Volume 252 (2012) no. 5, p. 3630 | DOI:10.1016/j.jde.2011.11.017
Guo, Yuxia; Tang, Zhongwei Multibump bound states for quasilinear Schrödinger systems with critical frequency, Journal of Fixed Point Theory and Applications, Volume 12 (2012) no. 1-2, p. 135 | DOI:10.1007/s11784-012-0092-1
Wu, Tsung-Fang Two coupled nonlinear Schrödinger equations involving a non-constant coupling coefficient, Nonlinear Analysis: Theory, Methods Applications, Volume 75 (2012) no. 13, p. 4766 | DOI:10.1016/j.na.2012.03.027
Liu, Zuhan Rotating multicomponent Bose–Einstein condensates, Nonlinear Differential Equations and Applications NoDEA, Volume 19 (2012) no. 1, p. 49 | DOI:10.1007/s00030-011-0117-2
Ikoma, Norihisa; Tanaka, Kazunaga A local mountain pass type result for a system of nonlinear Schrödinger equations, Calculus of Variations and Partial Differential Equations, Volume 40 (2011) no. 3-4, p. 449 | DOI:10.1007/s00526-010-0347-x
Liu, Zuhan The spatial behavior of rotating two-component Bose–Einstein condensates, Journal of Functional Analysis, Volume 261 (2011) no. 6, p. 1711 | DOI:10.1016/j.jfa.2011.05.017
Tang, Zhongwei Spike-layer solutions to singularly perturbed semilinear systems of coupled Schrödinger equations, Journal of Mathematical Analysis and Applications, Volume 377 (2011) no. 1, p. 336 | DOI:10.1016/j.jmaa.2010.11.001
Zhang, Shan; Liu, Zuhan; Lin, Zhigui Global minimizers of coexistence for rotating -component Bose–Einstein condensates, Nonlinear Analysis: Real World Applications, Volume 12 (2011) no. 5, p. 2567 | DOI:10.1016/j.nonrwa.2011.03.006
Cao, Daomin; Chern, I-Liang; Wei, Jun-Cheng On ground state of spinor Bose–Einstein condensates, Nonlinear Differential Equations and Applications NoDEA, Volume 18 (2011) no. 4, p. 427 | DOI:10.1007/s00030-011-0102-9
Liu, Zuhan Rotating Two-Component Bose-Einstein Condensates, Acta Applicandae Mathematicae, Volume 110 (2010) no. 1, p. 367 | DOI:10.1007/s10440-008-9417-x
Kim, Kwang Ik; Liu, Zuhan Bose–Einstein Condensates with Non-classical Vortex, Acta Applicandae Mathematicae, Volume 110 (2010) no. 3, p. 1137 | DOI:10.1007/s10440-009-9498-1
Jing, Long; Jianfu, Yang Positive solutions for weakly coupled nonlinear elliptic systems, Acta Mathematica Scientia, Volume 30 (2010) no. 5, p. 1577 | DOI:10.1016/s0252-9602(10)60151-8
Ma, Li; Liu, Baiyu Symmetry results for decay solutions of elliptic systems in the whole space, Advances in Mathematics, Volume 225 (2010) no. 6, p. 3052 | DOI:10.1016/j.aim.2010.05.022
Weth, Tobias; Dancer, E.N.; Wei, Juncheng A priori bounds versus multiple existence of positive solutions for a nonlinear Schrödinger system, Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Volume 27 (2010) no. 3, p. 953 | DOI:10.1016/j.anihpc.2010.01.009
Bartsch, Thomas; Dancer, Norman; Wang, Zhi-Qiang A Liouville theorem, a-priori bounds, and bifurcating branches of positive solutions for a nonlinear elliptic system, Calculus of Variations and Partial Differential Equations, Volume 37 (2010) no. 3-4, p. 345 | DOI:10.1007/s00526-009-0265-y
Ma, Li; Schulze, B.-W. Blow-up Theory for the Coupled L 2-Critical Nonlinear Schrödinger System in the Plane, Milan Journal of Mathematics, Volume 78 (2010) no. 2, p. 591 | DOI:10.1007/s00032-010-0131-6
Chen, Wenxiong; Li, Congming Classification of positive solutions for nonlinear differential and integral systems with critical exponents, Acta Mathematica Scientia, Volume 29 (2009) no. 4, p. 949 | DOI:10.1016/s0252-9602(09)60079-5
Zhongxue, Lü; Zuhan, Liu Sharp thresholds of two-components Bose–Einstein condensates, Computers Mathematics with Applications, Volume 58 (2009) no. 8, p. 1608 | DOI:10.1016/j.camwa.2009.07.022
Liu, Zuhan Phase separation of two-component Bose–Einstein condensates, Journal of Mathematical Physics, Volume 50 (2009) no. 10 | DOI:10.1063/1.3243875
Wei, Juncheng; Weth, Tobias Radial Solutions and Phase Separation in a System of Two Coupled Schrödinger Equations, Archive for Rational Mechanics and Analysis, Volume 190 (2008) no. 1, p. 83 | DOI:10.1007/s00205-008-0121-9
Wei, Gongming Existence and concentration of ground states of coupled nonlinear Schrödinger equations with bounded potentials, Chinese Annals of Mathematics, Series B, Volume 29 (2008) no. 3, p. 247 | DOI:10.1007/s11401-007-0104-4
Liu, Zhaoli; Wang, Zhi-Qiang Multiple Bound States of Nonlinear Schrödinger Systems, Communications in Mathematical Physics, Volume 282 (2008) no. 3, p. 721 | DOI:10.1007/s00220-008-0546-x
Liu, Zuhan Two-component Bose–Einstein condensates, Journal of Mathematical Analysis and Applications, Volume 348 (2008) no. 1, p. 274 | DOI:10.1016/j.jmaa.2008.07.033
Ma, Li; Zhao, Lin Sharp thresholds of blow-up and global existence for the coupled nonlinear Schrödinger system, Journal of Mathematical Physics, Volume 49 (2008) no. 6 | DOI:10.1063/1.2939238
Wei, Juncheng; Weth, Tobias Asymptotic behaviour of solutions of planar elliptic systems with strong competition, Nonlinearity, Volume 21 (2008) no. 2, p. 305 | DOI:10.1088/0951-7715/21/2/006
Li, Congming; Ma, Li Uniqueness of Positive Bound States to Schrödinger Systems with Critical Exponents, SIAM Journal on Mathematical Analysis, Volume 40 (2008) no. 3, p. 1049 | DOI:10.1137/080712301
Sirakov, Boyan Least Energy Solitary Waves for a System of Nonlinear Schrödinger Equations in $R^{n}$ , Communications in Mathematical Physics, Volume 271 (2007) no. 1, p. 199 | DOI:10.1007/s00220-006-0179-x
Lin, Tai-Chia; Wei, Juncheng Ground State of N Coupled Nonlinear Schrodinger Equations in $R^{n}, n \leq 3$ , Communications in Mathematical Physics, Volume 277 (2007) no. 2, p. 573 | DOI:10.1007/s00220-007-0365-5
Wei, Gong-Ming Existence and concentration of ground states of coupled nonlinear Schrödinger equations, Journal of Mathematical Analysis and Applications, Volume 332 (2007) no. 2, p. 846 | DOI:10.1016/j.jmaa.2006.09.083
Lin, Tai-Chia; Wei, Juncheng Half-Skyrmions and spike-vortex solutions of two-component nonlinear Schrödinger systems, Journal of Mathematical Physics, Volume 48 (2007) no. 5 | DOI:10.1063/1.2722559
Lin, Tai-Chia; Wei, Juncheng Spikes in two-component systems of nonlinear Schrödinger equations with trapping potentials, Journal of Differential Equations, Volume 229 (2006) no. 2, p. 538 | DOI:10.1016/j.jde.2005.12.011
Lin, Tai-Chia; Wei, Juncheng Symbiotic bright solitary wave solutions of coupled nonlinear Schrödinger equations, Nonlinearity, Volume 19 (2006) no. 12, p. 2755 | DOI:10.1088/0951-7715/19/12/002
Lin, Tai-Chia; Wei, Juncheng Solitary and self-similar solutions of two-component system of nonlinear Schrödinger equations, Physica D: Nonlinear Phenomena, Volume 220 (2006) no. 2, p. 99 | DOI:10.1016/j.physd.2006.07.009

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