linear control system, 51-67Cauchy problem, 52-54controllability, 55-62Korteweg-de Vries equation, 65—67transport equation, 62-65adjoint operator, 373a d ^ y (definition), 130admissibility condition, 52, see also regularity propertyapproximate controllability, 55, 57, 61Ascoli's theorem, 152, 170attractor, 280averaging, 332-333 backstepping, 334-337, ...

In this paper, four compelling numerical approaches, namely, the split-step Fourier transform (SSFT), pseudospectral method (FPSM), Crank-Nicolson (CNM), and Hopscotch (HSM), are exhaustively presented for solving 1D nonlinear Schrodinger equation (NLSE). The significance of is referred to its notable contribution in modeling wave propagation a plethora crucial real-life applications such as fi...

<p style='text-indent:20px;'>In this paper, we prove existence and orbital stability results of periodic standing waves for the cubic-quintic nonlinear Schrödinger equation. We use implicit function theorem to construct a smooth curve explicit with <i>dnoidal</i> profile such construction can be used that associated period map is strictly increasing in terms energy levels. The...

The existence of "dispersion-managed solitons," i.e., stable pulsating solitary-wave solutions to the nonlinear Schrodinger equation with periodically modulated and sign-variable dispersion is now well known in nonlinear optics. Our purpose here is to investigate whether similar structures exist for other well-known nonlinear wave models. Hence, here we consider as a basic model the variable-co...

We consider the periodic standing waves in derivative nonlinear Schrodinger (DNLS) equation arising plasma physics. By using a newly developed algebraic method with two eigenvalues, we classify all terms of eight eigenvalues Kaup-Newell spectral problem located at end points bands outside real line. The analytical work is complemented numerical approximation bands, this enables us to fully char...

A propagation method for time-dependent Schrodinger equations with an explicitly time-dependent Hamiltonian is developed where time ordering is achieved iteratively. The explicit time dependence of the time-dependent Schrodinger equation is rewritten as an inhomogeneous term. At each step of the iteration, the resulting inhomogeneous Schrodinger equation is solved with the Chebychev propagation...