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Functionals with values in the non‐archimedean field of laurent series and their applications to the equations of elasticity theory. I

    M. Radyna Affiliation

Abstract

Functionals with values in Non‐Archimedean field of Laurent series applied to the definition of generalized solution (in the form of soliton) of the Hopf equation. Calculation method for the profile of infinitely narrow soliton is proposed. Applying this method, calculations of profiles are reduced to the nonlinear system of algebraic equations in R n+1n > 1. It is shown that there is a possibility to find out some of the solutions of this system using the Newton iteration method. Example and numerical test are considered.


Funkcionalai su reikšmėmis ne-Archmediniuose Laurent'o sekų laukuose ir jų taikymas
elastiškumo teorijos lygtims


Santrauka. Funkcionalai su reikšmėmis ne‐Archimediniuose Laurent‘o seku laukuose pritaikyti apibrėžti apibendrintąjį Hop‘o lygties sprendinį solitono pavidalu. Pasiūlytas skaitinis algoritmas be galo siauro solitono profilio radimui. Taikant šį metodą, profilio radimas suvedamas į netiesinės algebrinių lygčių sistemos erdvėje Rn+ 1, n > 1, sprendimą. Parodyta, kad kai kuriuos sprendinius galima surasti naudojant Niutono iteracinį metodą. Pateikiami pavyzdžiai ir skaitiniai testai.


First Published Online: 14 Oct 2010

Keyword : generalized functions, distributions, conservation law, Hopf equation, soliton, shock waves

How to Cite
Radyna, M. (2002). Functionals with values in the non‐archimedean field of laurent series and their applications to the equations of elasticity theory. I. Mathematical Modelling and Analysis, 7(2), 297-312. https://doi.org/10.3846/13926292.2002.9637201
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Dec 15, 2002
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