Geodesic
On multi-lump solutions to the non-linear Schrödinger equation
Electronic journal of differential equations, Tome 1998 (1998)
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.
Classification : 35J60, 35Q55
Keywords: non-linear Schrödinger equation, semi-classical bound state, nonlinear-elliptic equation 
@article{EJDE_1998__1998__a1,
     author = {Magnus,  Robert},
     title = {On multi-lump solutions to the non-linear {Schr\"odinger} equation},
     journal = {Electronic journal of differential equations},
     year = {1998},
     volume = {1998},
     zbl = {0907.35046},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a1/}
}
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%J Electronic journal of differential equations
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Magnus,  Robert. On multi-lump solutions to the non-linear Schrödinger equation. Electronic journal of differential equations, Tome 1998 (1998). http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a1/