Collapse for the Generalized Three-Dimensional Nonlocal Nonlinear Schrödinger Equations

Advanced Nonlinear Studies ◽

10.1515/ans-2014-0314 ◽

2014 ◽

Vol 14 (3) ◽

Author(s):

Xin Jiang ◽

Zaihui Gan

Keyword(s):

A Priori Estimates ◽

A Priori ◽

Three Dimensional ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Nonlocal Terms ◽

Nonlocal Nonlinear

AbstractFinite time collapse of solutions to the generalized three-dimensional nonlocal nonlinear Schrödinger equations is studied. This result is achieved through establishing some a priori estimates for the nonlocal terms and by introducing a type of virial identities.

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Collisional dynamics of solitons in the coupled PT symmetric nonlocal nonlinear Schrödinger equations

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2017.04.011 ◽

2017 ◽

Vol 52 ◽

pp. 1-10 ◽

Author(s):

P.S. Vinayagam ◽

R. Radha ◽

U. Al Khawaja ◽

Liming Ling

Keyword(s):

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Collisional Dynamics ◽

Nonlocal Nonlinear

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Nonstandard bilinearization and interaction phenomenon for PT-symmetric coupled nonlocal nonlinear Schrödinger equations

Applied Mathematics Letters ◽

10.1016/j.aml.2020.106209 ◽

2020 ◽

Vol 103 ◽

pp. 106209 ◽

Author(s):

Fajun Yu ◽

Rui Fan

Keyword(s):

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Nonlocal Nonlinear ◽

Interaction Phenomenon

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Dynamics of high-order solitons in the nonlocal nonlinear Schrödinger equations

Nonlinear Dynamics ◽

10.1007/s11071-018-4373-0 ◽

2018 ◽

Vol 94 (1) ◽

pp. 489-502 ◽

Author(s):

Bo Yang ◽

Yong Chen

Keyword(s):

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Nonlocal Nonlinear

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Nonlocal nonlinear Schrödinger equations and their soliton solutions

Journal of Mathematical Physics ◽

10.1063/1.4997835 ◽

2018 ◽

Vol 59 (5) ◽

pp. 051501 ◽

Author(s):

Metin Gürses ◽

Aslı Pekcan

Keyword(s):

Soliton Solutions ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Nonlocal Nonlinear

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Three-dimensional spatiotemporal vector solitary waves in coupled nonlinear Schrödinger equations with variable coefficients

Journal of the Optical Society of America B ◽

10.1364/josab.30.000113 ◽

2012 ◽

Vol 30 (1) ◽

pp. 113 ◽

Author(s):

Si-Liu Xu ◽

Milivoj R. Belić ◽

Wei-Ping Zhong

Keyword(s):

Solitary Waves ◽

Three Dimensional ◽

Variable Coefficients ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Coupled Nonlinear Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Coupled Nonlinear Schrodinger Equations

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Multilinear eigenfunction estimates and global existence for the three dimensional nonlinear Schrödinger equations

Annales Scientifiques de l École Normale Supérieure ◽

10.1016/j.ansens.2004.11.003 ◽

2005 ◽

Vol 38 (2) ◽

pp. 255-301 ◽

Author(s):

N BURQ ◽

P GERARD ◽

N TZVETKOV

Keyword(s):

Global Existence ◽

Three Dimensional ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Eigenfunction Estimates

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New classes of solutions in the coupled PT symmetric nonlocal nonlinear Schrödinger equations with four wave mixing

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2017.11.016 ◽

2018 ◽

Vol 59 ◽

pp. 387-395 ◽

Author(s):

P.S. Vinayagam ◽

R. Radha ◽

U. Al Khawaja ◽

Liming Ling

Keyword(s):

Four Wave Mixing ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Wave Mixing ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Nonlocal Nonlinear

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Publisher's Note: Exact solutions to three-dimensional generalized nonlinear Schrödinger equations with varying potential and nonlinearities [Phys. Rev. E80, 036607 (2009)]

Physical Review E ◽

10.1103/physreve.80.049903 ◽

2009 ◽

Vol 80 (4) ◽

Author(s):

Zhenya Yan ◽

V. V. Konotop

Keyword(s):

Exact Solutions ◽

Three Dimensional ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Exact solutions to three-dimensional generalized nonlinear Schrödinger equations with varying potential and nonlinearities

Physical Review E ◽

10.1103/physreve.80.036607 ◽

2009 ◽

Vol 80 (3) ◽

Author(s):

Zhenya Yan ◽

V. V. Konotop

Keyword(s):

Exact Solutions ◽

Three Dimensional ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Two (2+1)-dimensional integrable nonlocal nonlinear Schrödinger equations: Breather, rational and semi-rational solutions

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2018.06.029 ◽

2018 ◽

Vol 114 ◽

pp. 99-107 ◽

Author(s):

Yulei Cao ◽

Boris A. Malomed ◽

Jingsong He

Keyword(s):

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Rational Solutions ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Nonlocal Nonlinear

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