A CONSERVATIVE DIFFERENCE SCHEME FOR SCHRODINGER NONLINEAR EQUATION

Yu.F. Kir´yanov, M.L. Kudryavtseva, N.V. Maslov, I.V. Shestakova
VANT. Ser.: Mat. Mod. Fiz. Proc 1999. Вып.1. С. 53-60.

      The study is made of a finite-difference scheme with the second order approximation for Schrodinger nonlinear equation, which conserves two first motion integrals. The conservation of these integrals in a bounded domain for Schrodinger 2-D nonlinear equation is demonstrated and the results comparative computations for two problems with a proposed scheme and a splitting scheme are presented. The computations were carried out of a collision of two solitons in 1-D problem and of a zero Gauss mode reflection in the medium without saturation in 2-D problem.