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We study properties of nonlinear magnetic fluctuations in the turbulent boundary layer (TBL) over polar cusps during a typical TBL crossing on 19 June 1998. Interball-1data in the summer TBL are compared with that of Geotail in solar wind (SW) and Polar in the northern TBL. In the TBL two characteristic slopes are seen: ~ - 1 at (0.004- 0.08) Hz and ~ - 2.2 at (0.08-2) Hz. We present evidences that random current sheets with features of coherent solitons can result in: (i) slopes of ~ - 1 in the magnetic power spectra; (ii) demagnetization of the SW plasma in "diamagnetic bubbles"; (iii) nonlinear, presumably, 3-wave phase coupling with cascade features; (iiii) departure from the Gaussian statistics. We discuss the above TBL properties in terms of intermittency and self-organization of nonlinear systems, and compare them with kinetic simulations of reconnected current sheet at the nonlinear state. Virtual satellite data in the model current sheet reproduce valuable cascade-like spectral and bi-spectral properties of the TBL turbulence.