Existence and Stability of Traveling Waves for Discrete Nonlinear Schrödinger Equations Over Long Times

SIAM Journal on Mathematical Analysis ◽

10.1137/18m1186484 ◽

2019 ◽

Vol 51 (3) ◽

pp. 1607-1656

Author(s):

Joackim Bernier ◽

Erwan Faou

Keyword(s):

Traveling Waves ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Discrete Nonlinear Schrödinger Equations ◽

Existence And Stability

Download Full-text

Homoclinic solutions of discrete nonlinear Schrödinger equations with unbounded potentials

Applied Mathematics Letters ◽

10.1016/j.aml.2021.107575 ◽

2021 ◽

pp. 107575

Author(s):

Ben-Xing Zhou ◽

Chungen Liu

Keyword(s):

Nonlinear Schrödinger Equations ◽

Homoclinic Solutions ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Discrete Nonlinear Schrödinger Equations

Download Full-text

Choreographies in the discrete nonlinear Schrödinger equations

The European Physical Journal Special Topics ◽

10.1140/epjst/e2018-00135-x ◽

2018 ◽

Vol 227 (5-6) ◽

pp. 615-624 ◽

Author(s):

Renato Calleja ◽

Eusebius Doedel ◽

Carlos García-Azpeitia ◽

Carlos L. Pando L.

Keyword(s):

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Discrete Nonlinear Schrödinger Equations

Download Full-text

Soliton dynamics in linearly coupled discrete nonlinear Schrödinger equations

Mathematics and Computers in Simulation ◽

10.1016/j.matcom.2009.08.033 ◽

2009 ◽

Vol 80 (4) ◽

pp. 814-824 ◽

Author(s):

A. Trombettoni ◽

H.E. Nistazakis ◽

Z. Rapti ◽

D.J. Frantzeskakis ◽

P.G. Kevrekidis

Keyword(s):

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Soliton Dynamics ◽

Nonlinear Schrodinger Equations ◽

Discrete Nonlinear Schrödinger Equations

Download Full-text

Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity: some results and open problems

Journées Équations aux dérivées partielles ◽

10.5802/jedp.71 ◽

2010 ◽

pp. 1-22 ◽

Author(s):

Mihai Mariş

Keyword(s):

Traveling Waves ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Open Problems ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Conditions At Infinity

Download Full-text

Standing waves for discrete nonlinear Schrödinger equations: sign-changing nonlinearities

Applicable Analysis ◽

10.1080/00036811.2011.609987 ◽

2011 ◽

Vol 92 (2) ◽

pp. 308-317 ◽

Author(s):

Alexander Pankov

Keyword(s):

Standing Waves ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Discrete Nonlinear Schrödinger Equations

Download Full-text

Gram determinant solutions to nonlocal integrable discrete nonlinear Schrödinger equations via the pair reduction

Wave Motion ◽

10.1016/j.wavemoti.2019.102487 ◽

2020 ◽

Vol 93 ◽

pp. 102487 ◽

Author(s):

Junchao Chen ◽

Bao-Feng Feng ◽

Yongyang Jin

Keyword(s):

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Discrete Nonlinear Schrödinger Equations ◽

Gram Determinant

Download Full-text

Localized states in discrete nonlinear Schrödinger equations

Physical Review Letters ◽

10.1103/physrevlett.72.591 ◽

1994 ◽

Vol 72 (5) ◽

pp. 591-595 ◽

Author(s):

David Cai ◽

A. R. Bishop ◽

Niels Grønbech-Jensen

Keyword(s):

Nonlinear Schrödinger Equations ◽

Localized States ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Discrete Nonlinear Schrödinger Equations

Download Full-text

Ground state solutions for periodic discrete nonlinear Schrödinger equations with saturable nonlinearities

Advances in Difference Equations ◽

10.1186/s13662-018-1574-2 ◽

2018 ◽

Vol 2018 (1) ◽

Author(s):

Luyu Zhang ◽

Shiwang Ma

Keyword(s):

Ground State ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Ground State Solutions ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Discrete Nonlinear Schrödinger Equations

Download Full-text

A discrete Adomian decomposition method for discrete nonlinear Schrödinger equations

Applied Mathematics and Computation ◽

10.1016/j.amc.2007.07.055 ◽

2008 ◽

Vol 197 (1) ◽

pp. 190-205 ◽

Author(s):

Athanassios Bratsos ◽

Matthias Ehrhardt ◽

Ioannis Th. Famelis

Keyword(s):

Decomposition Method ◽

Adomian Decomposition Method ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Adomian Decomposition ◽

Nonlinear Schrodinger Equations ◽

Discrete Nonlinear Schrödinger Equations

Download Full-text

Multiplicity results of breathers for the discrete nonlinear Schrödinger equations with unbounded potentials

Science China Mathematics ◽

10.1007/s11425-014-4883-2 ◽

2014 ◽

Vol 58 (4) ◽

pp. 781-790 ◽

Author(s):

Zhan Zhou ◽

DeFang Ma

Keyword(s):

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Multiplicity Results ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Discrete Nonlinear Schrödinger Equations

Download Full-text