  Functionals with values in Non-Archimedean field of Laurent series applied to
the definition of generalized solution (in the form of soliton and shock wave)
of the Hopf equation and equations of elasticity theory. Calculation method for
the profile of infinitely narrow soliton and shock wave is proposed. Applying
this method, calculations of profiles are reduced to the nonlinear system of
algebraic equations in $\mathbf{R}^{n+1}$, $n>1$. It is shown that there is a
possibility to find out some of the solutions of this system using the Newton
iteration method. Examples and numerical tests are considered.
