Functionals with values in Non‐Archimedean field of Laurent series applied to the definition of generalized solution (in the form of shock wave) of the Hopf equation and equations of elasticity theory. Calculation method for the profile of shock wave is proposed. 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.
Funkcionalai su reikšmėmis ne-Archmediniuose Laurent'o sekų laukuose ir jų taikymai elastiškumo teorijos lygtimis
Sanrtauka. Funkcionalai su reikšmėmis ne‐archimediniuose Laurent ‘o sekų laukuose pritaikyti apibrėžti apibendrintąjį Hop‘o lygties sprendinį solitono pavidalu. Pasiūlytas skaitinis algoritmas begalo 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.
Radyna, M. (2003). Functionals with values in the non‐Archimedean field of Laurent series and their applications to the equations of elasticity theory. II. Mathematical Modelling and Analysis, 8(1), 63-76. https://doi.org/10.3846/13926292.2003.9637211
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