The problem of generation of atomic soliton trains in elongated Bose-Einstein
condensates is considered in framework of Whitham theory of modulations of
nonlinear waves. Complete analytical solution is presented for the case when
the initial density distribution has sharp enough boundaries. In this case the
process of soliton train formation can be viewed as a nonlinear Fresnel
diffraction of matter waves. Theoretical predictions are compared with results
of numerical simulations of one- and three-dimensional Gross-Pitaevskii
equation and with experimental data on formation of Bose-Einstein bright
solitons in cigar-shaped traps.Comment: 8 pages, 3 figure