Applied Mathematical Sciences
Volume 1 / 1971 to Volume 204 / 2020
手机体育投注平台 Book Series
Volume 1 / 1971 to Volume 204 / 2020
手机体育投注平台 Book
手机体育投注平台 Chapter
In this chapter we describe the basic ingredients of the direct and inverse scattering problems for the matrix Schrödinger equation on the half line with the general self-adjoint boundary condition. We show ho...
手机体育投注平台 Chapter
手机体育投注平台 In this chapter the scattering process is described physically and mathematically, and the definition of the scattering operator is provided in terms of the wave operators introduced by Møller. The role of the...
手机体育投注平台 Chapter
手机体育投注平台 In this chapter we illustrate the theory presented earlier via explicitly solved examples. It is shown how the Marchenko integral equation can yield explicitly solved examples when its kernel contains a matrix...
手机体育投注平台 Chapter
In this introductory chapter the goals of the monograph are described, the contents of the remaining chapters and Appendix A are outlined, and the relevant general refer...
Chapter
手机体育投注平台 In this chapter we present the solution to the direct scattering problem for the half-line matrix Schrödinger equation using an input data set consisting of a matrix potential and a self-adjoint boundary condi...
Chapter
In this chapter we analyze the inverse scattering problem of recovery of the corresponding input data set D in the Faddeev class from a scattering data set S手机体育投注平台 in the Marchenko class. We discuss the nonuniqueness a...
Living Reference Work Entry In depth手机体育投注平台
Reference Work Entry In depth手机体育投注平台
Glossary
手机体育投注平台 Chapter and Conference Paper
A review of a recent method is presented to construct certain exact solutions to the focusing nonlinear Schrödinger equation on the line with a cubic nonlinearity. With motivation by the inverse scattering tra...
Reference Work Entry In depth手机体育投注平台
手机体育投注平台
Chapter and Conference Paper
The inverse scattering problem is reviewed for determining the cross sectional area of a human vocal tract. Various data sets are examined resulting from a unit-amplitude, monochromatic, sinusoidal volume velo...
Chapter and Conference Paper
The inverse scattering problem for the one-dimensional Schrödinger equation is considered when the potential is real valued and integrable and has a finite first-moment and no bound states. Corresponding to su...
Chapter and Conference Paper
In this review paper, the Korteweg-de Vries equation (KdV) is considered, and it is derived by using the Lax method and the AKNS method. An outline of the inverse scattering problem and of its solution is pres...
Article
A direct and inverse scattering theory on the full line is developed for a class of first-order selfadjoint 2n×2n手机体育投注平台 systems of differential equations with integrable potential matrices. Various properties of the co...
手机体育投注平台 Article
The inverse scattering problem arising in wave propagation in one-dimensional non-conservative media is analyzed. This is done in the frequency domain by considering the Schrödinger equation with the potentialikP...
Chapter
In this review paper, the generalized Schrödinger equation % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1...
Chapter and Conference Paper
The generalized one-dimensional Schrödinger equation d ^{2} ψ/dx ^{2}+k ^{2} H(x)^{2} ψ = Q(x)ψ is considered, where H(x) → 1 and Q(x) → 0 a...
手机体育投注平台 Chapter
The generalized one-dimensional Schrödinger equation \(\frac{{d^2 \psi }}{{dx^2 }} + k^2 H(x)^2 \psi = Q(x)\psi\) 手机体育投注平台 is consi...