%0 Journal Article
%T On multi-lump solutions to the non-linear Schrodinger equation
%A Robert Magnus
%J Electronic Journal of Differential Equations
%D 1998
%I Texas State University
%X We present a new approach to proving the existence of semi-classical bound states of the non-linear Schrodinger equation which are concentrated near a finite set of non-degenerate critical points of the potential function. The method is based on considering a system of non-linear elliptic equations. The positivity of the solutions is considered. It is shown how the same method yields ``multi-bump'' solutions ``homoclinic'' to an equilibrium point for non-autonomous Hamiltonian equations. The method provides a calculable asymptotic form for the solutions in terms of a small parameter.
%K Non-linear Schrodinger equation
%K semi-classical bound state
%K nonlinear-elliptic equation.
%U http://ejde.math.txstate.edu/Volumes/1998/29/abstr.html