Cauchy problem for higher-order Schrödinger equations in anisotropic Sobolev space

Applicable Analysis ◽

10.1080/00036810903277127 ◽

2009 ◽

Vol 88 (9) ◽

pp. 1329-1338 ◽

Author(s):

Cuihua Guo ◽

Xiangqing Zhao ◽

Xuemei Wei

Keyword(s):

Cauchy Problem ◽

Sobolev Space ◽

Higher Order ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Anisotropic Sobolev Space

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Well-posedness of Cauchy problem of fourth-order Schrödinger equations in anisotropic Sobolev space

Applied Mathematics and Computation ◽

10.1016/j.amc.2007.01.072 ◽

2007 ◽

Vol 190 (1) ◽

pp. 583-589 ◽

Author(s):

Cuihua Guo ◽

Shangbin Cui

Keyword(s):

Cauchy Problem ◽

Sobolev Space ◽

Fourth Order ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Anisotropic Sobolev Space

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Unique continuation through hyperplane for higher order parabolic and Schrödinger equations

Communications in Partial Differential Equations ◽

10.1080/03605302.2021.1881110 ◽

2021 ◽

pp. 1-75

Author(s):

Tianxiao Huang

Keyword(s):

Unique Continuation ◽

Higher Order ◽

Schrodinger Equations ◽

Schrödinger Equations

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Nondegenerate solitons for coupled higher-order nonlinear Schrödinger equations in optical fibers

Physica Scripta ◽

10.1088/1402-4896/ac0869 ◽

2021 ◽

Author(s):

YueJin Cai ◽

Jian wen Wu ◽

LangTao Hu ◽

Ji Lin

Keyword(s):

Optical Fibers ◽

Higher Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Modulation instability in higher-order nonlinear Schrödinger equations

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/1.5053941 ◽

2018 ◽

Vol 28 (12) ◽

pp. 123116 ◽

Author(s):

Amdad Chowdury ◽

Adrian Ankiewicz ◽

Nail Akhmediev ◽

Wonkeun Chang

Keyword(s):

Modulation Instability ◽

Higher Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Global existence and asymptotic behavior of the Cauchy problem for fourth-order Schrödinger equations with combined power-type nonlinearities

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2012.03.028 ◽

2012 ◽

Vol 392 (2) ◽

pp. 111-122 ◽

Author(s):

Cuihua Guo

Keyword(s):

Cauchy Problem ◽

Asymptotic Behavior ◽

Global Existence ◽

Fourth Order ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

The Cauchy Problem

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Dark solitons in N-coupled higher order nonlinear Schrödinger equations

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2006.07.014 ◽

2008 ◽

Vol 13 (7) ◽

pp. 1318-1328 ◽

Author(s):

P. Seenuvasakumaran ◽

A. Mahalingam ◽

K. Porsezian

Keyword(s):

Higher Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Dark Solitons ◽

Nonlinear Schrodinger Equations

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Higher order exponential time differencing scheme for system of coupled nonlinear Schrödinger equations

Applied Mathematics and Computation ◽

10.1016/j.amc.2013.11.089 ◽

2014 ◽

Vol 228 ◽

pp. 271-291 ◽

Author(s):

Harish P. Bhatt ◽

Abdul Q.M. Khaliq

Keyword(s):

Higher Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Coupled Nonlinear Schrödinger Equations ◽

Exponential Time ◽

Exponential Time Differencing ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

Coupled Nonlinear Schrodinger Equations

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Notes on the Cauchy problem for the self-adjoint and non-self-adjoint Schrödinger equations with polynomially growing potentials

Journal of Pseudo-Differential Operators and Applications ◽

10.1007/s11868-019-00301-6 ◽

2019 ◽

Vol 11 (2) ◽

pp. 703-731 ◽

Author(s):

Wataru Ichinose ◽

Takayoshi Aoki

Keyword(s):

Cauchy Problem ◽

The Self ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

The Cauchy Problem

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Integrability and soliton-like solutions for the coupled higher-order nonlinear Schrödinger equations with variable coefficients in inhomogeneous optical fibers

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2013.09.003 ◽

2014 ◽

Vol 19 (6) ◽

pp. 1783-1791 ◽

Author(s):

Yu-Feng Wang ◽

Bo Tian ◽

Min Li ◽

Pan Wang ◽

Ming Wang

Keyword(s):

Optical Fibers ◽

Variable Coefficients ◽

Higher Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations

10.1201/b17415 ◽

2014 ◽

Author(s):

Victor A. Galaktionov ◽

Enzo L. Mitidieri ◽

Stanislav I. Pohozaev

Keyword(s):

Blow Up ◽

Higher Order ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Hyperbolic Dispersion

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