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 ◽

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

Download Full-text

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 ◽

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

Download Full-text

Asymptotics for a class of oscillating fourth-order nonlinear Schrödinger equations

Journal of Mathematical Physics ◽

10.1063/1.5031825 ◽

2018 ◽

Vol 59 (7) ◽

pp. 071511

Author(s):

T. Saanouni

Keyword(s):

Fourth Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

Download Full-text

Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equations of fourth order in dimensions d⩾9

Journal of Differential Equations ◽

10.1016/j.jde.2011.08.009 ◽

2011 ◽

Vol 251 (12) ◽

pp. 3381-3402 ◽

Author(s):

Changxing Miao ◽

Guixiang Xu ◽

Lifeng Zhao

Keyword(s):

Fourth Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

Download Full-text

Global well-posedness and scattering for the fourth order nonlinear Schrödinger equations with small data in modulation and Sobolev spaces

Journal de Mathématiques Pures et Appliquées ◽

10.1016/j.matpur.2015.09.005 ◽

2016 ◽

Vol 105 (1) ◽

pp. 31-65 ◽

Author(s):

Michael Ruzhansky ◽

Baoxiang Wang ◽

Hua Zhang

Keyword(s):

Fourth Order ◽

Sobolev Spaces ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

Download Full-text

Wellposedness for the fourth order nonlinear Schrödinger equations

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2005.06.091 ◽

2006 ◽

Vol 320 (1) ◽

pp. 246-265 ◽

Author(s):

Chengchun Hao ◽

Ling Hsiao ◽

Baoxiang Wang

Keyword(s):

Fourth Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

Download Full-text

On the Cauchy problem of fourth-order nonlinear Schrödinger equations

Nonlinear Analysis ◽

10.1016/j.na.2006.04.020 ◽

2007 ◽

Vol 66 (12) ◽

pp. 2911-2930 ◽

Author(s):

Ai Guo ◽

Shangbin Cui

Keyword(s):

Cauchy Problem ◽

Fourth Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

The Cauchy Problem

Download Full-text

Riemann‐Hilbert approach for multisoliton solutions of generalized coupled fourth‐order nonlinear Schrödinger equations

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.5964 ◽

2019 ◽

Vol 43 (2) ◽

pp. 865-880 ◽

Author(s):

Tai‐Yang Xu ◽

Shou‐Fu Tian ◽

Wei‐Qi Peng

Keyword(s):

Fourth Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Multisoliton Solutions

Download Full-text

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 ◽

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

Download Full-text

Vector multi-rogue waves for the three-coupled fourth-order nonlinear Schrödinger equations in an alpha helical protein

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2018.06.014 ◽

2019 ◽

Vol 67 ◽

pp. 49-59 ◽

Author(s):

Zhong Du ◽

Bo Tian ◽

Han-Peng Chai ◽

Yu-Qiang Yuan

Keyword(s):

Fourth Order ◽

Rogue Waves ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Helical Protein

Download Full-text

Semirational rogue waves for the three-coupled fourth-order nonlinear Schrödinger equations in an alpha helical protein

Superlattices and Microstructures ◽

10.1016/j.spmi.2017.09.046 ◽

2017 ◽

Vol 112 ◽

pp. 362-373 ◽

Author(s):

Zhong Du ◽

Bo Tian ◽

Qi-Xing Qu ◽

Han-Peng Chai ◽

Xiao-Yu Wu

Keyword(s):

Fourth Order ◽

Rogue Waves ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Helical Protein

Download Full-text