Numerical simulations of parity-time symmetric nonlinear Schrödinger equations in critical case
DOI10.3934/dcdss.2020411OpenAlexW3043077336MaRDI QIDQ2063976
Paul Nuiro, Edès Destyl, Jacques Laminie, Pascal Poullet
Publication date: 3 January 2022
Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.3934/dcdss.2020411
finite difference methodCrank-Nicolson schemenumerical simulationsnonlinear Schrödinger equationsparity-time symmetryblow up solution
Asymptotic behavior of solutions to PDEs (35B40) Theory of programming languages (68N15) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Schrödinger operator, Schrödinger equation (35J10) Blow-up in context of PDEs (35B44) Time-dependent Schrödinger equations and Dirac equations (35Q41) Numerical analysis (65-XX)
Cites Work
- The Cauchy problem for coupled nonlinear Schrödinger equations with linear damping: local and global existence and blowup of solutions
- The focusing nonlinear Schrödinger equation: Effect of the coupling to a low frequency field
- Nonlinear Schrödinger equations and sharp interpolation estimates
- Analytical and numerical aspects of certain nonlinear evolution equations. II. Numerical, nonlinear Schrödinger equation
- Global existence of solutions to coupled \(\mathcal{PT}\)-symmetric nonlinear Schrödinger equations
- Coupled pendula chains under parametric \(\mathcal{PT}\)-symmetric driving force
- Critical blowup in coupled parity-time-symmetric nonlinear Schrödinger equations
- A perfectly matched layer approach to the nonlinear Schrödinger wave equations
- Supercritical Blowup in Coupled Parity-Time-Symmetric Nonlinear Schrödinger Equations
- On the Global Behavior of Solutions of a Coupled System of Nonlinear Schrödinger Equation
- Transparent and absorbing boundary conditions for the schrödinger equation in a bounded domain
- Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
- BLOW-UP IN TWO-COMPONENT NONLINEAR SCHRÖDINGER SYSTEMS WITH AN EXTERNAL DRIVEN FIELD
- Artificial boundary conditions for one-dimensional cubic nonlinear Schrödinger equations
- Introduction to nonlinear dispersive equations
- Numerical simulation of coupled nonlinear Schrödinger equation
- Implementation of transparent boundaries for numerical solution of the Schröder equation.
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