Application of homotopy perturbation Sumudu transform method to linear and nonlinear Schrödinger equations

2016 ◽  
Author(s):  
Zeynep Fidan Koçak ◽  
Dilara Altan Koç
Keyword(s):  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Transform Method ◽  
Nonlinear Schrödinger ◽  
Homotopy Perturbation ◽  
Nonlinear Schrodinger Equations ◽  
Sumudu Transform ◽  
Linear And Nonlinear

Application of the Homotopy Perturbation Method to Linear and Nonlinear Schrödinger Equations

2008 ◽  
Vol 63 (3-4) ◽  
pp. 140-144 ◽  
Author(s):  
Mohamed M. Mousaa ◽  
Shahwar F. Ragab
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Analytic Treatment ◽  
Nonlinear Schrödinger ◽  
Homotopy Perturbation ◽  
Nonlinear Schrodinger Equations ◽  
Linear And Nonlinear

He’s homotopy perturbation method (HPM) is applied to linear and nonlinear Schrödinger equations for obtaining exact solutions. The HPM is used for an analytic treatment of these equations. The results reveal that the HPM is very effective, convenient and quite accurate to such types of partial differential equations.

Short Time Behavior of Solutions to Linear and Nonlinear Schrödinger Equations

2008 ◽  
Vol 60 (5) ◽  
pp. 1168-1200 ◽  
Author(s):  
Michael Taylor
Keyword(s):  
Broad Class ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Time Behavior ◽  
Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Pinsky Phenomenon ◽  
Nonlinear Schrodinger Equations ◽  
Linear And Nonlinear ◽  
Short Time

AbstractWe examine the fine structure of the short time behavior of solutions to various linear and nonlinear Schrödinger equations ut = iΔu+q(u) on I×ℝn, with initial data u(0, x) = f (x). Particular attention is paid to cases where f is piecewise smooth, with jump across an (n−1)-dimensional surface. We give detailed analyses of Gibbs-like phenomena and also focusing effects, including analogues of the Pinsky phenomenon. We give results for general n in the linear case. We also have detailed analyses for a broad class of nonlinear equations when n = 1 and 2, with emphasis on the analysis of the first order correction to the solution of the corresponding linear equation. This work complements estimates on the error in this approximation.

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