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Functionals with values in the Non-Archimedean field of Laurent series and their applications to the equations of elasticity theory

Mikalai Radyna
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Abstract

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.

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Mikalai Radyna. 2002-04-17. Functionals with values in the Non-Archimedean field of Laurent series and their applications to the equations of elasticity theory. https://arxiv.org/abs/math-ph/0204037

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