Second Approximation of Theory of Short Waves

Within the framework of the theory of short waves an asymptotic solution being the second approximation solution to a problem of determination of excess pressure at the front of one-dimensional shock waves is obtained, which does not reduce to a mere addition of members proportional to squares of their arguments into the first approximation solution with exception of a case of flat symmetry. The comparison of calculations using the obtained solution with the numerical results for a flat wave of a triangular profile shows that using the second approximation for the calculation of excess pressure at the front of a shock wave allows a range of applicability of the shock wave theory to be greatly expanded. Meanwhile the first approximation solution provides the higher accuracy in calculations of the compression duration in the wave.