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

Abstract

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 reikšmemis ne‐archimediniuose Laurent ‘o seku laukuose pritaikyti apibrežti apibendrintaji Hop'o lygties sprendini solitono pavidalu. Pasiūlytas skaitinis algoritmas begalo siauro solitono profilio radimui. Taikant ši metoda, profilio radimas suvedamas j netiesines algebriniu lygčiu sistemos erdveje R n+1, n > 1, sprendima. Parodyta, kad kai kuriuos sprendinius galima surasti naudojant Niutono iteracini metoda. Pateikiami pavyzdžiai ir skaitiniai testai. First Published Online: 14 Oct 2010

Keywords

• generalized functions
• distributions
• conservation law
• Hopf equation
• equations of elasticity theory
• soliton