Note on a paper of E. M. E. Zayed and S. F. M. Ibraham.
Numerical computation of solitons for optical systems
In this paper, we present numerical methods for the determination of solitons, that consist in spatially localized stationary states of nonlinear scalar equations or coupled systems arising in nonlinear optics. We first use the well-known shooting method in order to find excited states (characterized by the number of nodes) for the classical nonlinear Schrödinger equation. Asymptotics can then be derived in the limits of either large are large nonlinear exponents . In a second part, we compute...
Numerical computation of solitons for optical systems
In this paper, we present numerical methods for the determination of solitons, that consist in spatially localized stationary states of nonlinear scalar equations or coupled systems arising in nonlinear optics. We first use the well-known shooting method in order to find excited states (characterized by the number k of nodes) for the classical nonlinear Schrödinger equation. Asymptotics can then be derived in the limits of either large k are large nonlinear exponents σ. In a second part, we compute...
Numerical computation of the eigenvalues for the spheroidal wave equation with accurate error estimation by matrix method.
Numerical methods for approximating eigenvalues of boundary value problems.
Numerische Behandlung von Verzweigungsproblemen bei gewöhnlichen Differentialgleichungen.
O локализации собственных чисел одной спектральной задачи.
On a certain boundary value problem for a fourth-order iterated differential equation
On a certain modification of Sturm's comparison theorem
On a Five-Diagonal Jacobi Matrices and Orthogonal Polynomials on Rays in the Complex Plane
∗ Partially supported by Grant MM-428/94 of MESC.Systems of orthogonal polynomials on the real line play an important role in the theory of special functions [1]. They find applications in numerous problems of mathematical physics and classical analysis. It is known, that classical polynomials have a number of properties, which uniquely define them.
On a non-self adjoint eigenfunction expansion.
On a non-self adjoint expansion formula.
On a q-deformed harmonic oscillator with variable linear momentum.
On an example of phase-space tunneling
On an inverse scattering problem for a discontinuous Sturm-Liouville equation with a spectral parameter in the boundary condition.
On Bojarski's index formula for nonsmooth interfaces.
On convergence of orthogonal series of Bessel functions
On discreteness of spectrum of a functional differential operator
We study conditions of discreteness of spectrum of the functional-differential operator on . In the absence of the integral term this operator is a one-dimensional Schrödinger operator. In this paper we consider a symmetric operator with real spectrum. Conditions of discreteness are obtained in terms of the first eigenvalue of a truncated operator. We also obtain one simple condition for discreteness of spectrum.
On Floquet eigenvalue problems for first order differential systems in the complex domain.
On Hill's equation with a discontinuous coefficient.