Svoystva Gravitatsionnogo I Elektromagnitnogo Polya : Analogiya mezhdu jelektromagnitnym i gravitacionnym polem

Uravneniya matematicheskoy fiziki pri bol'shikh energiyakh stanovyatsya nelineynymi. V dannoy knige issledovano uravnenie OTO, i pokazano, chto pri bol'shikh energiyakh ono imeet schetnoe kolichestvo resheniy so schetnym kolichestvom energii sostoyaniya, impul'sa i momenta impul'sa. Kak pokazano v knige uravnenie Shredingera i Kleyna-Gordona svodyatsya k ne relyativistskomu i relyativistskomu nelineynomu uravneniyu Nav'e - Stoksa s mnimoy kinematicheskoy vyazkost'yu i/(2m). Pri etom nelineynoe uravnenie Nav'e - Stoksa v turbulentnom rezhime imeet schetnoe kolichestvo resheniy s schetnym kolichestvom sobstvennykh energiy. Eto pozvolyaet provesti klassifikatsiyu nelineynykh uravneniy. Imeetsya dva rezhima resheniya nelineynykh uravneniy, laminarnyy i turbulentnyy rezhim v sluchae gidrodinamiki, svobodnoe i svyazannoe sostoyanie v sluchae uravneniy kvantovoy mekhaniki. Pervoe sostoyanie obladaet nepreryvnoy energiey i resheniem, a vtoroe schetnym znacheniem energii i kolichestvom resheniy. Mezhdu dvumya rezhimami sushchestvuet rezkaya granitsa, polozhitel'naya i otritsatel'naya energiya v kvantovoy mekhaniki, deystvitel'nym i kompleksnym resheniem v gidrodinamike. Granitsa opredelyaetsya kriticheskim chislom Reynol'dsa i nulevoy energiey sostoyaniya.