Long-time asymptotic behavior of a mixed Schrödinger equation with weighted Sobolev initial data

Long–time Asymptotics for Solutions of the Nls Equation with Initial Data in a Weighted Sobolev Space

Here Γ is the gamma function and the function r is the so-called reflection coefficient for the potential q0(x) = q(x, t = 0), as described below. The error term O( log t t ) is uniform for all x ∈ R. The above asymptotic form was first obtained in [ZaMa], but without the error estimate. Based on the nonlinear steepest descent method introduced in [DZ1], the error estimate in (1.1) was derived ...

Cauchy Problem of Nonlinear Schrödinger Equation with Initial Data in Sobolev Space W

In this paper, we consider in R the Cauchy problem for nonlinear Schrödinger equation with initial data in Sobolev space W s,p for p < 2. It is well known that this problem is ill posed. However, We show that after a linear transformation by the linear semigroup the problem becomes locally well posed in W s,p for 2n n+1 < p < 2 and s > n(1− 1 p ). Moreover, we show that in one space dimension, ...

Cauchy problem of nonlinear Schrödinger equation with initial data in Sobolev space W s , p for p < 2

In this paper, we consider in R the Cauchy problem for nonlinear Schrödinger equation with initial data in Sobolev space W s,p for p < 2. It is well known that this problem is ill posed. However, We show that after a linear transformation by the linear semigroup the problem becomes locally well posed in W s,p for 2n n+1 < p < 2 and s > n(1− 1 p ). Moreover, we show that in one space dimension, ...

Ja n 20 04 Schrödinger equation with critical Sobolev exponent

Numerical solution for one-dimensional independent of time Schrödinger Equation

In this paper, one of the numerical solution method of one- particle, one dimensional timeindependentSchrodinger equation are presented that allows one to obtain accurate bound state eigenvalues and functions for an arbitrary potential energy function V(x).For each case, we draw eigen functions versus the related reduced variable for the correspondingenergies. The paper ended with a comparison ...