Solitons and their stability in high dispersive systems. I. Fourth-order nonlinear Schrödinger-type equations with power-law nonlinearities

Solitons and other solutions to nonlinear Schrödinger equation with fourth-order dispersion and dual power law nonlinearity using several different techniques

The European Physical Journal Plus ◽

10.1140/epjp/i2017-11527-4 ◽

2017 ◽

Vol 132 (6) ◽

Cited By ~ 15

Author(s):

Elsayed M. E. Zayed ◽

Abdul-Ghani Al-Nowehy ◽

Mona E. M. Elshater

Keyword(s):

Schrödinger Equation ◽

Power Law ◽

Fourth Order ◽

Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Order Dispersion ◽

Dual Power

Optical and other solitons for the fourth-order dispersive nonlinear Schrödinger equation with dual-power law nonlinearity

Superlattices and Microstructures ◽

10.1016/j.spmi.2017.03.022 ◽

2017 ◽

Vol 105 ◽

pp. 183-197 ◽

Cited By ~ 69

Author(s):

Maysaa Mohamed Al Qurashi ◽

Abdullahi Yusuf ◽

Aliyu Isa Aliyu ◽

Mustafa Inc

Keyword(s):

Schrödinger Equation ◽

Power Law ◽

Fourth Order ◽

Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Dual Power

Exact solutions for the fourth order nonlinear Schrodinger equations with cubic and power law nonlinearities

Mathematical and Computer Modelling ◽

10.1016/j.mcm.2005.08.010 ◽

2006 ◽

Vol 43 (7-8) ◽

pp. 802-808 ◽

Cited By ~ 49

Author(s):

Abdul-Majid Wazwaz

Keyword(s):

Exact Solutions ◽

Power Law ◽

Fourth Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

Lyapunov approach to the soliton stability in highly dispersive systems. I. Fourth order nonlinear Schrödinger equations

Physics Letters A ◽

10.1016/0375-9601(96)00231-9 ◽

1996 ◽

Vol 215 (5-6) ◽

pp. 254-256 ◽

Cited By ~ 11

Author(s):

V.I. Karpman

Keyword(s):

Fourth Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Lyapunov Approach ◽

Nonlinear Schrödinger ◽

Dispersive Systems ◽

Nonlinear Schrodinger Equations ◽

Soliton Stability

A compact split step Padé scheme for higher-order nonlinear Schrödinger equation (HNLS) with power law nonlinearity and fourth order dispersion

Computer Physics Communications ◽

10.1016/j.cpc.2010.10.016 ◽

2011 ◽

Vol 182 (2) ◽

pp. 366-371 ◽

Cited By ~ 12

Author(s):

Moussa Smadi ◽

Derradji Bahloul

Keyword(s):

Schrödinger Equation ◽

Power Law ◽

Fourth Order ◽

Schrodinger Equation ◽

Higher Order ◽

Nonlinear Schrödinger ◽

Order Dispersion

Erratum to: “Lyapunov approach to the soliton stability in highly dispersive systems. I. Fourth order nonlinear Schrödinger equations” [Phys. Lett. A 215 (1996) 257–259]

Physics Letters A ◽

10.1016/s0375-9601(99)00275-3 ◽

1999 ◽

Vol 256 (5-6) ◽

pp. 422 ◽

Cited By ~ 1

Author(s):

V.I Karpman

Keyword(s):

Fourth Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Lyapunov Approach ◽

Nonlinear Schrödinger ◽

Dispersive Systems ◽

Nonlinear Schrodinger Equations ◽

Soliton Stability

On the inhomogeneous fourth-order nonlinear Schrödinger equation

Journal of Mathematical Physics ◽

10.1063/1.4929657 ◽

2015 ◽

Vol 56 (9) ◽

pp. 093502 ◽

Cited By ~ 11

Author(s):

Nakao Hayashi ◽

Pavel I. Naumkin

Keyword(s):

Schrödinger Equation ◽

Fourth Order ◽

Schrodinger Equation ◽

Nonlinear Schrödinger

Stability of one and two-dimensional spatial solitons in a cubic-quintic-septimal nonlinear Schrödinger equation with fourth-order diffraction and PT-symmetric potentials

Wave Motion ◽

10.1016/j.wavemoti.2021.102810 ◽

2021 ◽

pp. 102810

Author(s):

Boubakary Abdou ◽

Fabien II Ndzana ◽

Latchio Tiofack Gaston ◽

Alidou Mohamadou

Keyword(s):

Schrödinger Equation ◽

Fourth Order ◽

Schrodinger Equation ◽

Two Dimensional ◽

Spatial Solitons ◽

Nonlinear Schrödinger ◽

Order Diffraction

Fourth-order dispersive systems on the one-dimensional torus

Journal of Pseudo-Differential Operators and Applications ◽

10.1007/s11868-015-0112-1 ◽

2015 ◽

Vol 6 (2) ◽

pp. 237-263 ◽

Cited By ~ 2

Author(s):

Hiroyuki Chihara

Keyword(s):

Fourth Order ◽

Dimensional Torus ◽

One Dimensional ◽

Dispersive Systems ◽

The One

Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation in negative Sobolev spaces

Journal of Functional Analysis ◽

10.1016/j.jfa.2021.109150 ◽

2021 ◽

pp. 109150

Author(s):

Tadahiro Oh ◽

Kihoon Seong

Keyword(s):

Schrödinger Equation ◽

Fourth Order ◽

Sobolev Spaces ◽

Schrodinger Equation ◽

Gaussian Measures ◽

Nonlinear Schrödinger ◽

Negative Sobolev Spaces