scholarly journals A combination of multiscale time integrator and two-scale formulation for the nonlinear Schrödinger equation with wave operator

2017 ◽  
Vol 326 ◽  
pp. 320-336 ◽  
Author(s):  
Xiaofei Zhao
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Wave Operator ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger

scholarly journals Compact Local Structure-Preserving Algorithms for the Nonlinear Schrödinger Equation with Wave Operator

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Langyang Huang ◽  
Zhaowei Tian ◽  
Yaoxiong Cai
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Wave Operator ◽  
Schrodinger Equation ◽  
Convergence Rates ◽  
Nonlinear Schrodinger Equation ◽  
Local Conservation ◽  
Structure Preserving ◽  
Nonlinear Schrödinger ◽  
Local Momentum

Combining the compact method with the structure-preserving algorithm, we propose a compact local energy-preserving scheme and a compact local momentum-preserving scheme for the nonlinear Schrödinger equation with wave operator (NSEW). The convergence rates of both schemes are Oh4+τ2. The discrete local conservative properties of the presented schemes are derived theoretically. Numerical experiments are carried out to demonstrate the convergence order and local conservation laws of the developed algorithms.

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