TY - RPRT
T1 - Solutions to the nonlinear Schroedinger equation carrying momentum along a curve. Part II: proof of the existence result
Y1 - 2007
A1 - Fethi Mahmoudi
A1 - Andrea Malchiodi
AB - We prove existence of a special class of solutions to the (elliptic) Nonlinear Schroedinger Equation $- \\\\epsilon^2 \\\\Delta \\\\psi + V(x) \\\\psi = |\\\\psi|^{p-1} \\\\psi$ on a manifold or in the Euclidean space. Here V represents the potential, p is an exponent greater than 1 and $\\\\epsilon$ a small parameter corresponding to the Planck constant. As $\\\\epsilon$ tends to zero (namely in the semiclassical limit) we prove existence of complex-valued solutions which concentrate along closed curves, and whose phase in highly oscillatory. Physically, these solutions carry quantum-mechanical momentum along the limit curves. In the first part of this work we identified the limit set and constructed approximate solutions, while here we give the complete proof of our main existence result.
UR - http://hdl.handle.net/1963/2111
U1 - 2578
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -