A nonlinear differential equation is derived which describes the propagation of axisymmetric stationary longitudinal-bending\nwaves in infinite cylindrical shell of Timoshenko type, interacting with the external nonlinear elastic medium. A modified\nperturbation method based on the use of diagonal Pade approximants was applied to build exact solitary-wave solutions of the\nderived equation in the form of traveling front and the traveling pulse. Numerical solutions of the equation, obtained by means of\nfinite difference method, are in good agreement with the corresponding exact analytical ones.
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