20.500.12556/RUL-103652 O nelinearnih valovih delo diplomskega seminarja On nonlinear waves V delu diplomskega seminarja se posvetimo posameznim nelinearnim parcialnim diferencialnim enačbam različnih redov. Najprej predstavimo metodo reševanja kvazilinearnih parcialnih diferencialnih enačb, metodo karakteristik in izrek, ki pod določenimi pogoji zagotavlja lokalno enolično rešljivost teh enačb. Na primeru Eulerjeve enačbe predstavimo problem neenoličnosti globalne rešitve pri reševanju z metodo karakteristik. Enačbo zapišemo v obliki ohranitvenega zakona in predstavimo rešitev s pomočjo udarnih valov. V nadaljevanju se posvetimo enačbam z disperzijo in vplivu disperzije na obliko udarnih valov. Predstavimo rešitev Burgersove enačbe s pomočjo Hopf-Coleove transformacije. Delo zaključimo s predstavitvijo preproste, enosolitonske rešitve Korteweg-deVriesove enačbe. This thesis is dedicated to the analysis of certain nonlinear partial differential equations of different orders. We begin with the method of characteristics. We show how the method is used for solving quasilinear partial differential equations. We also state the existence theorem which tells us under which conditions there exists a unique local solution. Using the example of Euler equation, the problem of non-uniqueness of the solution, constructed by means of the characteristics, is presented. The equation is written in the form of a conservation law and the solution is constructed by introducing the shock waves. We continue by focusing on the equations with dispersion and we study its impact on the shape of shock waves. We present the solution of Burgers equation using the Hopf-Cole transformation. The thesis is concluded by the presentation of a simple singlesoliton solution of the Korteweg-deVries equation. metoda karakteristik transportna enačba ohranitveni zakon udarni val Burgersova enačba Korteweg-deVriesova enačba soliton method of characteristics transport equation conservation law shock wave Burgers' equation Korteweg-deVries equation soliton true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2018-09-21 07:45:02 2018-09-21 07:45:03 2022-08-16 03:43:27 0000-00-00 00:00:00 2018 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.9 91316 18457177 473.pdf 473.pdf 1 EA53361C78132F775B5DCDE7442CEC64 778a546fd948e2260547dd457056e6009bd2670dfb3f9cd631bd003a6b4bf467 de22da90-a1b5-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=114118 474.zip 474.zip 1 D8B38650110E22F57B29FED83918350E 2e98f17a43df4d56c153f000eb33881eaf0595ea1f036267426a74bdce12daa9 de3f7426-a1b5-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=114120 Fakulteta za matematiko in fiziko 0 0 0