ABSTRACT
Abstract The constant-profile solutions of an acoustic pulse that propagates in a nonlinear hereditary medium without a form distortion are constructed by means of a direct algebraic method. To satisfy the boundary conditions, for a special type of infinite series describing solution derived the new formulae for inversion of such series are obtained. By using algebraic method, it is shown that the equations considered allow the existence of two types of the solitary waves whose velocities depend on the value of its amplitude jump discontinuity across the wave front. These the constant-profile waves propagate with the velocities both less or greater than the velocity of sound in the linear medium.
