Journal of Nonlinear Science

, Volume 17, Issue 4, pp 349–367 | Cite as

Soliton Splitting by External Delta Potentials

  • J. HolmerEmail author
  • J. MarzuolaEmail author
  • M. ZworskiEmail author


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.


External Potential Strichartz Estimate Bright Soliton Discrete Breather Inverse Scattering Method 
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Copyright information

© Springer 2007

Authors and Affiliations

  1. 1.Mathematics Department, University of California, Evans HallBerkeley, CA 94720USA

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