The static equilibrium state in axial compressive force was taken as reference configuration

the propagation property of nonlinear wave in an axially compressed cylindrical shell subjected to radial disturbance was studied.Using the logarithmic hoop strain to describe nonlinear strain-displacement relation

the nonlinear flexural wave equation governing axisymmetric radial motion of the cylindrical shell was derived.By means of the reductive perturbation technique(RPT)

the nonlinear Schro¨dinger equation(NLSE) was obtained from solvability condition.The cnoidal wave and envelope soliton solutions were given by the traveling-wave method.The existence conditions of bright soliton and dark soliton indicate that the axial stress has important effect on the propagation property of the nonlinear wave.Two-soliton solution is obtained by the so-called Hirota's bilinearization method.