One of the difficulties associated with the scattering problems arising in connection with integrable systems is that they are frequently non-self-adjoint, making it difficult to determine where the spectrum lies. In this paper, we consider the problem of locating and counting the discrete eigenvalues associated with the scattering problem for which the sine-Gordon equation is the isospectral f...

This paper concerns spectral stability and time evolution of N -solitons in the KdV hierarchy with mixed commuting time flows. Spectral stability problem is analyzed by using a pair of self-adjoint operators with finite numbers of negative eigenvalues. We show that the absence of unstable eigenvalues in the stability problem is related to the absence of negative eigenvalues of these operators i...

We revisit here the analytical continuation approach usually employed to compute quasinormal modes (QNM) and frequencies of a given potential barrier $V$ starting from bounded states respective eigenvalues Schroedinger operator associated with well corresponding inverted $-V$. consider an exactly soluble problem Poschl-Teller type defined behaved QNM spectrum, but for which $\cal H$ obtained by...

aim and background: this study seeks the effect of teaching problem solving on self-efficacy and perceived self-efficacy in adolescents.   methods and materials: in this quasi-experimental study using three group with pre-test and post-test, on hundred sixty students were randomly selected via multi-stage sampling, and were divided into 64 students of experimental group and 62 students of place...

In this paper, we study a singular Sturm–Liouville problem with an eigenparameter-dependent boundary condition and transmission conditions at two interior points. Using operator-theoretical formulation, transfer the to operator in appropriate Hilbert space. It is proved that self-adjoint. We also give asymptotic formulas of eigenvalues problem. Moreover, Green’s function discussed.

The initial-value problem for hyperbolic equation d2u(t)/dt2 +A(t)u(t) = f (t) (0 ≤ t ≤ T), u(0) = φ,u(0) = ψ in a Hilbert space H with the self-adjoint positive definite operators A(t) is considered. The second order of accuracy difference scheme for the approximately solving this initial-value problem is presented. The stability estimates for the solution of this difference scheme are establi...

Unlike the trapping of time-harmonic water waves by fixed obstacles, the oscillation of freely floating structures gives rise to a complex nonlinear spectral problem. Still, through a convenient elimination scheme the system simplifies to a linear spectral problem for a self-adjoint operator in a Hilbert space. Under symmetry assumptions on the geometry of the fluid domain, we present condition...