Magnus, Robert2019-03-252019-03-251998-11-15Magnus, R. (1998). On multi-lump solutions to the non-linear Schrodinger equation. <i>Electronic Journal of Differential Equations, 1998</i>(29), pp. 1-24.1072-6691https://hdl.handle.net/10877/7940We 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.Text24 pages1 file (.pdf)enAttribution 4.0 InternationalNon-linear Schrodinger equationSemi-classical bound stateNonlinear-elliptic equationArticle