Representation formula for traveling waves to a derivative nonlinear Schrödinger equation with the periodic boundary condition

Dynamical Systems and Differential Equations, AIMS Proceedings 2015 Proceedings of the 10th AIMS International Conference (Madrid, Spain) ◽

10.3934/proc.2015.0878 ◽

2015 ◽

Author(s):

Shoji Yotsutani ◽

Kunimochi Sakamoto ◽

Minoru Murai

Keyword(s):

Boundary Condition ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Traveling Waves ◽

Schrodinger Equation ◽

Periodic Boundary Condition ◽

Periodic Boundary ◽

Representation Formula ◽

Nonlinear Schrodinger Equation ◽

Derivative Nonlinear Schrödinger Equation

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On the Cauchy problem for the derivative nonlinear Schrodinger equation with periodic boundary condition

International Mathematics Research Notices ◽

10.1155/imrn/2006/96763 ◽

2006 ◽

Author(s):

S. Herr

Keyword(s):

Boundary Condition ◽

Cauchy Problem ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Periodic Boundary Condition ◽

Periodic Boundary ◽

Nonlinear Schrodinger Equation ◽

The Cauchy Problem ◽

Derivative Nonlinear Schrödinger Equation

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Global well-posedness of the derivative nonlinear Schrödinger equation with periodic boundary condition in H12

Journal of Differential Equations ◽

10.1016/j.jde.2017.05.026 ◽

2017 ◽

Vol 263 (8) ◽

pp. 4658-4722 ◽

Author(s):

Razvan Mosincat

Keyword(s):

Boundary Condition ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Periodic Boundary Condition ◽

Periodic Boundary ◽

Nonlinear Schrodinger Equation ◽

Well Posedness ◽

Nonlinear Schrödinger ◽

Derivative Nonlinear Schrödinger Equation

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Blow-up of solutions for the nonlinear Schrödinger equation with quartic potential and periodic boundary condition

Lecture Notes in Mathematics - Functional-Analytic Methods for Partial Differential Equations ◽

10.1007/bfb0084910 ◽

1990 ◽

pp. 236-251 ◽

Author(s):

Takayoshi Ogawa ◽

Yoshio Tsutsumi

Keyword(s):

Boundary Condition ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Periodic Boundary Condition ◽

Periodic Boundary ◽

Blow Up ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Quartic Potential

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THE FOCUSING NONLINEAR SCHRÖDINGER EQUATION ON THE QUARTER PLANE WITH TIME-PERIODIC BOUNDARY CONDITION: A RIEMANN–HILBERT APPROACH

Journal of the Institute of Mathematics of Jussieu ◽

10.1017/s1474748007000151 ◽

2007 ◽

Vol 6 (04) ◽

pp. 579 ◽

Author(s):

Anne Boutet de Monvel ◽

Vladimir Kotlyarov

Keyword(s):

Boundary Condition ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Periodic Boundary Condition ◽

Periodic Boundary ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Quarter Plane ◽

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On the derivative nonlinear Schrödinger equation on the half line with Robin boundary condition

Journal of Mathematical Physics ◽

10.1063/5.0049337 ◽

2021 ◽

Vol 62 (8) ◽

pp. 081502

Author(s):

Phan Van Tin

Keyword(s):

Boundary Condition ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Robin Boundary Condition ◽

Nonlinear Schrodinger Equation ◽

Half Line ◽

Nonlinear Schrödinger ◽

Derivative Nonlinear Schrödinger Equation ◽

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Long-time asymptotic behavior for the Gerdjikov-Ivanov type of derivative nonlinear Schrödinger equation with time-periodic boundary condition

Proceedings of the American Mathematical Society ◽

10.1090/proc/13917 ◽

2017 ◽

Vol 146 (4) ◽

pp. 1713-1729 ◽

Author(s):

Shou-Fu Tian ◽

Tian-Tian Zhang

Keyword(s):

Boundary Condition ◽

Asymptotic Behavior ◽

Schrodinger Equation ◽

Periodic Boundary Condition ◽

Periodic Boundary ◽

Nonlinear Schrodinger Equation ◽

Long Time ◽

Derivative Nonlinear Schrödinger Equation ◽

Time Periodic ◽

Time Asymptotic Behavior

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KAM for the derivative nonlinear Schrödinger equation with periodic boundary conditions

Journal of Differential Equations ◽

10.1016/j.jde.2013.11.007 ◽

2014 ◽

Vol 256 (4) ◽

pp. 1627-1652 ◽

Author(s):

Jianjun Liu ◽

Xiaoping Yuan

Keyword(s):

Schrödinger Equation ◽

Boundary Conditions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Periodic Boundary ◽

Periodic Boundary Conditions ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Derivative Nonlinear Schrödinger Equation

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Solving localized wave solutions of the derivative nonlinear Schrödinger equation using an improved PINN method

Nonlinear Dynamics ◽

10.1007/s11071-021-06554-5 ◽

2021 ◽

Author(s):

Juncai Pu ◽

Jun Li ◽

Yong Chen

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Wave Solutions ◽

Derivative Nonlinear Schrödinger Equation

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The data-driven localized wave solutions of the derivative nonlinear Schrödinger equation by using improved PINN approach

Wave Motion ◽

10.1016/j.wavemoti.2021.102823 ◽

2021 ◽

pp. 102823

Author(s):

Juncai Pu ◽

Weiqi Peng ◽

Yong Chen

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Data Driven ◽

Nonlinear Schrödinger ◽

Wave Solutions ◽

Derivative Nonlinear Schrödinger Equation

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Remarks on blow-up criteria for the derivative nonlinear Schrödinger equation under the optimal threshold setting

Journal of Differential Equations ◽

10.1016/j.jde.2021.05.003 ◽

2021 ◽

Vol 291 ◽

pp. 90-109

Author(s):

Hideo Takaoka

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Blow Up ◽

Nonlinear Schrodinger Equation ◽

Optimal Threshold ◽

Nonlinear Schrödinger ◽

Derivative Nonlinear Schrödinger Equation ◽

Threshold Setting

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