On Multi-Lump Solutions to the Non-Linear Schrodinger Equation
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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.
CitationMagnus, R. (1998). On multi-lump solutions to the non-linear Schrodinger equation. Electronic Journal of Differential Equations, 1998(29), pp. 1-24.
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