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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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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High-order semi-rational solutions for the coherently coupled nonlinear Schrödinger equations with the positive coherent coupling

Applied Mathematics Letters ◽

10.1016/j.aml.2020.106343 ◽

2020 ◽

Vol 105 ◽

pp. 106343 ◽

Author(s):

Gao-Qing Meng

Keyword(s):

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Coupled Nonlinear Schrödinger Equations ◽

Rational Solutions ◽

Nonlinear Schrödinger ◽

Coherent Coupling ◽

Nonlinear Schrodinger Equations ◽

Coupled Nonlinear Schrodinger Equations

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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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Symmetries and exact solutions of a class of nonlocal nonlinear Schrödinger equations with self-induced parity-time-symmetric potential

Physical Review E ◽

10.1103/physreve.91.042908 ◽

2015 ◽

Vol 91 (4) ◽

Author(s):

Debdeep Sinha ◽

Pijush K. Ghosh

Keyword(s):

Exact Solutions ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Symmetric Potential ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Nonlocal Nonlinear

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Multi-rogue waves and rational solutions of the coupled nonlinear Schrödinger equations

Nonlinear Analysis Real World Applications ◽

10.1016/j.nonrwa.2012.04.010 ◽

2013 ◽

Vol 14 (1) ◽

pp. 14-27 ◽

Author(s):

Bao-Guo Zhai ◽

Wei-Guo Zhang ◽

Xiao-Li Wang ◽

Hai-Qiang Zhang

Keyword(s):

Rogue Waves ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Coupled Nonlinear Schrödinger Equations ◽

Rational Solutions ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Coupled Nonlinear Schrodinger Equations

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On a class of nonlocal nonlinear Schrödinger equations and wave collapse

The European Physical Journal Special Topics ◽

10.1140/epjst/e2007-00217-5 ◽

2007 ◽

Vol 147 (1) ◽

pp. 343-362 ◽

Author(s):

M. Ablowitz ◽

I. Bakirtas ◽

B. Ilan

Keyword(s):

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Wave Collapse ◽

Nonlocal Nonlinear

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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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