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On the computation of the solution of perturbed nonlinear Schrödinger equations
Author(s) -
Subaşı Murat
Publication year - 2010
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20459
Subject(s) - maple , mathematics , nonlinear system , computation , partial derivative , partial differential equation , mathematical physics , function (biology) , schrödinger's cat , mathematical analysis , physics , quantum mechanics , algorithm , botany , evolutionary biology , biology
We introduce a numerical treatment for solving nonlinear Schrödinger equations in the form $i\, \psi_{t} + a_{0}\psi_{xx} - v (x) \psi - a_{1} |\psi|^{2}\psi = f (x, \, t),$ where f ( x , t ) is an arbitrary function, being perturbative, dependent on ψ . For this purpose, we developed a MAPLE ® procedure and examined the effectiveness of the method on two problems. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010