Electronic Journal of Differential Equations,
Vol. 1998(1998), No. 29, pp. 1-24.

Title: On  multi-lump solutions to the  non-linear Schrodinger equation 

Author: Robert Magnus (The Univ. Science Institute, Reykjavik, Iceland)

Abstract: 
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.


Submitted June 23, 1998. Published November 15, 1998.
Math Subject Classification: 35J60, 35Q55.
Key Words: Non-linear Schrodinger equation; semi-classical bound state; 
           nonlinear-elliptic equation.