w U ni versity of T echnolo gy K oszy kowa 75, 00-662 W arszawaIn the pap er the propagation of short pulses in nonli near K err-like me dium is considered . Pulses are describ ed by the nonlinear Schr odinger equation in w hich the generalizati on of nonlinear disp ersion term and the self-frequency shif t are taken into account. T he solution of the equation in the form of quadrature is derived. Both the phase and pro Ùle of the pulse intensity are obtained. T he cases of propagating bright and dark solitons in saturable K err-like medium are analyzed. T w o mo dels of saturation are considered. T he explic it analytical expressions describing the K err limit are rep orted. T he relations b etw een the medium and propagatio n parameters are thoroughly discussed .PACS numb ers: 42. 65. T g, 42. 82. Et 1. I n t r o d u ct io n I n no nl i near Kerr di electri c stro ng l i ght p ul ses of specia l shap e (sol i to ns) pro pagate wi tho ut changi ng i ts for m due to the com p ensati on of two e˜ects | the l i near gro up vel ocit y di spersion ( G V D ) and nonl i near p ol ari zati on of the medi um (self-pha se m odul atio n, SP M) [1{ 3]. Pro pagati on of these pul ses i s descri b ed by no nl i near Schr odi nger equa ti on (N LSE).The stro ng electri c Ùeld of sol i to n can cause ma ny other e˜ects in the Kerr di electri c. One of these e˜ects | the thi rd or hi gher order di spersion | i s l i near [4{ 6]; the others are no nl i near. In the pap er two of such e˜ects are considered | nonl i near di spersio n (ND ) [6{ 9] and self-frequency shif t (SFS) [10,11]. The NLSE equati on general i zed by these (G NLSE) term s al so p ossesse s sol uti ons i n the form of sol i to ns, but special requi rem ents b etween para m eters of the medi um and sol i to n are needed i n order to preserve the ori gina l pro Ùle fro m the pure Kerr di electri c [6, 12{ 16].In the presence of stro ng soli to n Ùeld the nonl i near perm i tti vi ty of the m edi um can devi ate fro m the sim pl e Kerr dep endence reveal ing satura ti o n. The wa y we shoul d m odi fy i t depends on m odel of satura ti on. By no w the tw o-level m odel [17], the exp onenti al mo del [18 ], \ square two-level" [19], and pol yno m ial (7 7)

-In the paper the propagation of temporal pulses through generalized saturable nonlinear Kerr-like media is described analytically. The influence of symmetry conditions on relations between phase and amplitude is analyzed. These relations introduced into a canonical description of propagation enable a solution of the Euler-Lagrange equations. The accuracy of a canonical description is discussed.

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