Bu çalışma, genelleştirilmiş lineer olmayan Schordinger (GNLS) denkleminin yüksek doğruluklu sayısal çözümünü elde etmek içindir. Çalışmada iki farklı zaman parçalanması kullanılacaktır. İlk doğruluğu olan ve literatürde iyi bilinen Crank-Nicolson yöntemi, ikinci ise tek adımlı dördüncü mertebeden doğruluğa sahip yöntemdir. Zaman için genel bir yöntem kullanıldıktan sonra konum septik B-spline ...

In this study, the finite difference method is applied to an optimal control problem controlled by two functions which are in the coefficients of two-dimensional Schrodinger equation. Convergence of the finite difference approximation according to the functional is proved. We have used the implicit method for solving the two-dimensional Schrodinger equation. Although the implicit scheme obtaine...

Focus Serial: Frontiers of Nonlinear Optics Several kinds of nonlinear optical effects have been observed in recent years using silicon waveguides, and their device applications are attracting considerable attention. In this review, we provide a unified theoretical platform that not only can be used for understanding the underlyin...

Motivated by a similar approach for Born-Oppenheimer molecular dynamics, this paper proposes an extended shadow Lagrangian density quantum states of superfluids. The contains additional field variable that is forced to follow the wave function state through rapidly oscillating harmonic oscillator. By considering adiabatic limit large frequencies oscillator, we can derive two equations motions, ...

The classical quantization of a Lienard-type nonlinear oscillator is achieved by scheme (M. C. Nucci. Theor. Math. Phys., 168:994–1001, 2011) that preserves the Noether point symmetries underlying Lagrangian in order to construct Schrodinger equation. This method straightforwardly yields equation momentum space as given (V. Chithiika Ruby, M. Senthilvelan, and Lakshmanan. J. Phys. A: Gen., 45:3...

The general form of the cubic Boussinesq-type equation is considered. In special cases, this reduced to three different versions Boussinesq equations and also generalized modified equation. Using slowly varying envelope approximation perturbation reduction method transformed coupled nonlinear Schrodinger two-component solitary wave solution obtained. Explicit analytical expressions for shape pa...

A systematic investigation of certain higher order or deformed soliton equations with (1 + 1) dimensions, from the point complete integrability, is presented. Following procedure Ablowitz, Kaup, Newell and Segur (AKNS) we find that version Nonlinear Schrodinger equation, Hirota equation AKNS admit Lax pairs. We report each identified possesses Painleve property for partial differential admits t...