Optimal distributed control problem for cubic nonlinear Schrödinger equation

Vega, Constanza Sánchez Fernández de la; Rial, Diego

doi:10.1007/s00498-018-0222-4

Cited by 3 publications

(1 citation statement)

References 25 publications

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“…There is a large amount of research on OCPs for Schrödinger equations without any specific gradient terms: for instance, in [16], the authors demonstrate the existence of an optimal control for the cubic nonlinear Schrödinger equation (NLSE) and give the optimality conditions. In [17], the authors study an OCP with a final functional for a standard linear Schrödinger equation (LSE), give an existence theorem for OCP, and also derive the necessary optimality conditions.…”

Section: Introductionmentioning

confidence: 99%

A Necessary Optimality Condition on the Control of a Charged Particle

Aksoy,

Celik,

Zengin

2024

Symmetry

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We consider an optimal control problem with the boundary functional for a Schrödinger equation describing the motion of a charged particle. By using the existence of an optimal solution, we search the necessary optimality conditions for the examined control problem. First, we constitute an adjoint problem by a Lagrange multiplier that is related to constraints of theory on symmetries and conservation laws. The adjoint problem obtained is a boundary value problem with a nonhomogeneous boundary condition. We prove the existence and uniqueness of the solution of the adjoint problem. Then, we demonstrate the differentiability of the objective functional in the sense of Frechet and get a formula for its gradient. Finally, we give a necessary optimality condition in the form of a variational inequality.

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Section: Introductionmentioning

confidence: 99%

A Necessary Optimality Condition on the Control of a Charged Particle

Aksoy,

Celik,

Zengin

2024

Symmetry

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Exact chirped solutions and chaotic behaviors of the high-order nonlinear Schrödinger equation with non-Kerr nonlinear terms and cubic-quintic-septic nonlinearities

2024

Phys. Scr.

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In this paper, we obtain the exact solutions and corresponding nonlinear chirps of the high-order nonlinear Schrödinger equation with non-Kerr nonlinear terms and cubic-quintic-septic nonlinearities based on the trial equation method and the complete discrimination system for polynomial. Speciﬁcally, we systematically solve all exact chirped solutions of the equation in its general form. Moreover, we discuss the chaotic behaviors of the model while considering the external perturbation terms.

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A generalized nonlinear cubic-quartic Schrodinger equation and its implications in quantum wire

El-Nabulsi

Anukool

2023

Eur. Phys. J. B

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Optimal distributed control problem for cubic nonlinear Schrödinger equation

Cited by 3 publications

References 25 publications

A Necessary Optimality Condition on the Control of a Charged Particle

A Necessary Optimality Condition on the Control of a Charged Particle

Exact chirped solutions and chaotic behaviors of the high-order nonlinear Schrödinger equation with non-Kerr nonlinear terms and cubic-quintic-septic nonlinearities

A generalized nonlinear cubic-quartic Schrodinger equation and its implications in quantum wire

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