On multi-lump solutions to the non-linear Schrodinger equation
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....
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| Format: | Article |
| Language: | English |
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Texas State University
1998-11-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/1998/29/abstr.html |
| Summary: | 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. |
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| ISSN: | 1072-6691 |