scholarly journals Long-time behavior of solutions to a fourth-order nonlinear Schrödinger equation with critical nonlinearity

2021 ◽  
Author(s):  
Mamoru Okamoto ◽  
Kota Uriya
Keyword(s):  
Fourth Order ◽  
Decay Estimate ◽  
The Self ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Self Similar Solution ◽  
Long Time ◽  
Self Similar

AbstractWe consider the long-time behavior of solutions to a fourth-order nonlinear Schrödinger (NLS) equation with a derivative nonlinearity. By using the method of testing by wave packets, we construct an approximate solution and show that the solution for the fourth-order NLS has the same decay estimate for linear solutions. We prove that the self-similar solution is the leading part of the asymptotic behavior.

scholarly journals ASYMPTOTIC BEHAVIOR OF NONLINEAR SCHRÖDINGER SYSTEMS WITH LINEAR COUPLING

2014 ◽  
Vol 11 (01) ◽  
pp. 159-183 ◽  
Author(s):  
PAOLO ANTONELLI ◽  
RADA MARIA WEISHÄUPL
Keyword(s):  
Asymptotic Behavior ◽  
Rabi Frequency ◽  
Original System ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Linear Coupling ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrödinger Systems ◽  
Long Time ◽  
Schrödinger Systems

A system of two coupled nonlinear Schrödinger equations is investigated. In addition, a linear coupling which models an external driven field described by the Rabi frequency is considered. Asymptotics for large Rabi frequency are carried out and the convergence in the appropriate Strichartz space is proven. As a consequence, the global existence for the limiting system yields us a criterion for the long time behavior of the original system.

scholarly journals On global dynamics of 2D convective Cahn–Hilliard equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Global Dynamics ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Initial Value ◽  
Hilliard Equation ◽  
Long Time ◽  
Cahn Hilliard Equation ◽  
Initial Boundary Value

AbstractIn this paper, we study the long time behavior of solution for the initial-boundary value problem of convective Cahn–Hilliard equation in a 2D case. We show that the equation has a global attractor in $H^{4}(\Omega )$ H 4 ( Ω ) when the initial value belongs to $H^{1}(\Omega )$ H 1 ( Ω ) .

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