Abstract: The general form of the nonlinear wave equation in a nonlinear elastic bar was derived．An asympto-tic solution of the solitary wave was obtained by means of the modified complete-approximate method and was numerically analyzed‚from which two kinds of solitary waves—the bel- l type solitary wave and the oscillatory-type solitary wavewere found．Theoretical and numerical analyses indicate that the solitary wave is caused by the action of the material nonlinearity and the lateral effect of the bar‚and that the propagation velocity of the solitary wave is related to its amplitude‚i．e．the larger the amplitude is‚the larger the propagation velocity is；and that the wave width is of inverse ratio with the square root of wave propagation velocity and is related to the parameter indicating the dispersion effect of the wave—the larger the propagation velocity is‚the shorter the wave width is．

Key words: nonlinear elastic bar, solitary wave, KdV-mKdV equation, numerical analysis