Electron. J. Diff. Eqns., Vol. 1998(1998), No. 29, pp. 1-24.
### On multi-lump solutions to the non-linear Schrodinger equation

Robert Magnus

**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.

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Robert Magnus

The University Science Institute

Dunhaga 3, 107-Reykjavik, Iceland.

e-mail: robmag@raunvis.hi.is

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