Soliton Splitting by External Delta Potentials |
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Authors: | J Holmer J Marzuola M Zworski |
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Institution: | (1) Mathematics Department, University of California, Evans Hall, Berkeley, CA 94720, USA |
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Abstract: | We show that in the dynamics of the nonlinear Schrodinger equation a soliton scattered by an external delta potential splits
into two solitons and a radiation term. Theoretical analysis gives the amplitudes and phases of the reflected and transmitted
solitons with errors going to zero as the velocity of the incoming soliton tends to infinity. Numerical analysis shows that
this asymptotic relation is valid for all but very slow solitons. We also show that the total transmitted mass, that is, the
square of the L2 norm of the solution restricted on the transmitted side of the delta potential, is in good agreement with the quantum transmission
rate of the delta potential. |
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Keywords: | |
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