On Solution of Nonlinear Cubic Non-Homogeneous Schrodinger Equation
El-Tawil, M., Nasr, S., El Zoheiry, H. (2011). On Solution of Nonlinear Cubic Non-Homogeneous Schrodinger Equation. EKB Journal Management System, 14(AEROSPACE SCIENCES & AVIATION TECHNOLOGY, ASAT - 14 – May 24 - 26, 2011), 1-16. doi: 10.21608/asat.2011.23245
Magdy A. El-Tawil; Sherif E. Nasr; H. El Zoheiry. "On Solution of Nonlinear Cubic Non-Homogeneous Schrodinger Equation". EKB Journal Management System, 14, AEROSPACE SCIENCES & AVIATION TECHNOLOGY, ASAT - 14 – May 24 - 26, 2011, 2011, 1-16. doi: 10.21608/asat.2011.23245
El-Tawil, M., Nasr, S., El Zoheiry, H. (2011). 'On Solution of Nonlinear Cubic Non-Homogeneous Schrodinger Equation', EKB Journal Management System, 14(AEROSPACE SCIENCES & AVIATION TECHNOLOGY, ASAT - 14 – May 24 - 26, 2011), pp. 1-16. doi: 10.21608/asat.2011.23245
El-Tawil, M., Nasr, S., El Zoheiry, H. On Solution of Nonlinear Cubic Non-Homogeneous Schrodinger Equation. EKB Journal Management System, 2011; 14(AEROSPACE SCIENCES & AVIATION TECHNOLOGY, ASAT - 14 – May 24 - 26, 2011): 1-16. doi: 10.21608/asat.2011.23245

On Solution of Nonlinear Cubic Non-Homogeneous Schrodinger Equation

International Conference on Aerospace Sciences and Aviation Technology
Article 24, Volume 14, AEROSPACE SCIENCES & AVIATION TECHNOLOGY, ASAT - 14 – May 24 - 26, 2011, May 2011, Page 1-16  XML PDF (298.92 K)
Document Type: Original Article
DOI: 10.21608/asat.2011.23245
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Authors
Magdy A. El-Tawil1; Sherif E. Nasr2; H. El Zoheiry1
1Engineering Mathematics Department, Faculty of Engineering, Cairo University, Giza, Egypt.
2Engineering Mathematics Department, Faculty of Engineering, Fayoum University, Fayoum, Egypt.
Abstract
In this paper, a perturbing nonlinear non-homogeneous Schrodinger equation is studied under limited time interval, complex initial conditions and zero Neumann conditions. The perturbation and Picard approximation methods together with the eigenfunction expansion and variational parameters methods are used to introduce an approximate solution for the perturbative nonlinear case for which a power series solution is proved to exist. Using Mathematica, the solution algorithm is tested through computing the possible orders of approximations. The method of solution is illustrated through case studies and figures.
Keywords
Nonlinear Schrodinger equation; perturbation; Eigenfunction expansion; Mathematica; Picard Approximation
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