On concentration of positive bound states of nonlinear Schrödinger equations

Communications in Mathematical Physics ◽

10.1007/bf02096642 ◽

1993 ◽

Vol 153 (2) ◽

pp. 229-244 ◽

Cited By ~ 285

Author(s):

Xuefeng Wang

Keyword(s):

Bound States ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Bound States of 2-D Nonlinear Schrödinger Equations with Potentials Tending to Zero at Infinity

SIAM Journal on Mathematical Analysis ◽

10.1137/110846919 ◽

2013 ◽

Vol 45 (4) ◽

pp. 2299-2331 ◽

Cited By ~ 2

Author(s):

Mingwen Fei ◽

Huicheng Yin

Keyword(s):

Bound States ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Orbital Stability of Bound States of Semiclassical Nonlinear Schrödinger Equations with Critical Nonlinearity

SIAM Journal on Mathematical Analysis ◽

10.1137/070683842 ◽

2008 ◽

Vol 40 (1) ◽

pp. 365-381 ◽

Cited By ~ 7

Author(s):

Tai-Chia Lin ◽

Juncheng Wei

Keyword(s):

Bound States ◽

Orbital Stability ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Critical Nonlinearity ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Nodal bound states with clustered spikes for Nonlinear Schrödinger equations

Acta Mathematica Scientia ◽

10.1016/s0252-9602(14)60133-8 ◽

2014 ◽

Vol 34 (6) ◽

pp. 1892-1906 ◽

Cited By ~ 1

Author(s):

Jinjun DAI ◽

Qihan HE ◽

Biwen LI

Keyword(s):

Bound States ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Bound states of nonlinear Schrödinger equations with potentials vanishing at infinity

Journal d Analyse Mathématique ◽

10.1007/bf02790279 ◽

2006 ◽

Vol 98 (1) ◽

pp. 317-348 ◽

Cited By ~ 61

Author(s):

A. Ambrosetti ◽

A. Malchiodi ◽

D. Ruiz

Keyword(s):

Bound States ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Multi-bump bound states of nonlinear Schrödinger equations with electromagnetic fields and critical frequency

Journal of Differential Equations ◽

10.1016/j.jde.2008.07.035 ◽

2008 ◽

Vol 245 (10) ◽

pp. 2723-2748 ◽

Cited By ~ 27

Author(s):

Zhongwei Tang

Keyword(s):

Electromagnetic Fields ◽

Bound States ◽

Critical Frequency ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Existence and concentration of bound states of a class of nonlinear Schrödinger equations in ℝ2 with potential tending to zero at infinity

Acta Mathematica Sinica English Series ◽

10.1007/s10114-012-0524-2 ◽

2012 ◽

Vol 28 (11) ◽

pp. 2243-2274 ◽

Cited By ~ 1

Author(s):

Da Cheng Cui ◽

Ji Hui Zhang ◽

Ming Wen Fei

Keyword(s):

Bound States ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Instability of bound states for abstract nonlinear Schrödinger equations

Journal of Functional Analysis ◽

10.1016/j.jfa.2011.03.010 ◽

2011 ◽

Vol 261 (1) ◽

pp. 90-110 ◽

Cited By ~ 19

Author(s):

Masahito Ohta

Keyword(s):

Bound States ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Uniqueness of positive bound states with multi-bump for nonlinear Schrödinger equations

Calculus of Variations and Partial Differential Equations ◽

10.1007/s00526-015-0930-2 ◽

2015 ◽

Vol 54 (4) ◽

pp. 4037-4063 ◽

Cited By ~ 15

Author(s):

Daomin Cao ◽

Shuanglong Li ◽

Peng Luo

Keyword(s):

Bound States ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Vector–soliton bound states for the coupled mixed derivative nonlinear Schrödinger equations in optical fibers

Wave Motion ◽

10.1016/j.wavemoti.2012.05.004 ◽

2013 ◽

Vol 50 (1) ◽

pp. 1-10 ◽

Cited By ~ 6

Author(s):

Min Li ◽

Jing-Hua Xiao ◽

Bo Qin ◽

Ming Wang ◽

Bo Tian

Keyword(s):

Optical Fibers ◽

Bound States ◽

Nonlinear Schrödinger Equations ◽

Mixed Derivative ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Vector Soliton

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Bound States of Envelope Solitons in Coupled Nonlinear Schrödinger Equations

Journal of Nonlinear Optical Physics & Materials ◽

10.1142/s0218863597000046 ◽

1997 ◽

Vol 06 (01) ◽

pp. 49-53 ◽

Cited By ~ 1

Author(s):

M. F. Mahmood ◽

W. W. Zachary ◽

T. L. Gill

Keyword(s):

Bound States ◽

Hamiltonian Formulation ◽

Bound State ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Coupled Nonlinear Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Coupled Nonlinear Schrodinger Equations

Interaction of strongly and weakly overlapping solitons of two independent modes is analyzed in the framework of a system of coupled nonlinear Schrödinger equations with oscillating terms. A Hamiltonian formulation is employed. Our analysis reveals that the solitons form a strongly bound state with their centers coincident and weakly bound states with their centers separated from each other.

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