Space-time Gevrey smoothing effect for the dissipative nonlinear Schrödinger equations

2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Gaku Hoshino
Keyword(s):  
Space Time ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Smoothing Effect ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations

scholarly journals A Space-Time Fully Decoupled Wavelet Galerkin Method for Solving Multidimensional Nonlinear Schrödinger Equations with Damping

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Jiaqun Wang ◽  
Youhe Zhou ◽  
Xiaojing Liu
Keyword(s):  
Space Time ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Test Problems ◽  
Wavelet Expansion ◽  
Schrödinger Equations ◽  
Bounded Interval ◽  
Nonlinear Schrödinger ◽  
Fine Mesh ◽  
Nonlinear Schrodinger Equations

On the basis of sampling approximation for a function defined on a bounded interval by combining Coiflet-type wavelet expansion and technique of boundary extension, a space-time fully decoupled formulation is proposed to solve multidimensional Schrödinger equations with generalized nonlinearities and damping. By applying a wavelet Galerkin approach for spatial discretization, nonlinear Schrödinger equations are first transformed into a system of ordinary differential equations, in which all matrices are completely independent of time and never need to be recalculated in the time integration. Then, the classical fourth-order explicit Runge–Kutta method is used to solve the resulting semidiscretization system. By studying several widely considered test problems, results demonstrate that when a relatively fine mesh is adopted, the present wavelet algorithm has a much better computational accuracy and efficiency than many existing numerical methods, due to its higher order of convergence in space which can go up to 6.

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