Korteweg-de Vries jednadžba

master's thesis

• Author: Ariana Trstenjak
• Mentor: Siniša Slijepčević (mentor)
• Committee member: Siniša Slijepčević (predsjednik povjerenstva)
• Committee member: Josip Tambača (član povjerenstva)
• Committee member: Nenad Antonić (član povjerenstva)
• Committee member: Marcela Hanzer (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2017-07-17, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu prikazana je egzistencija i jedinstvenost rješenja Korteweg-de Vries jednadžbe, određena svojstva i primjena iste. Prvo poglavlje rada definira kanonski oblik KdV jednadžbe, te nas kroz kratak povijesni slijed uvodi u daljnje razvijanje KdV jednadžbe. U drugom poglavlju uvode se osnovni pojmovi koji će biti potrebni za razumijevanje egzistencije i jedinstvenosti rješenja KdV jednadžbe. U trećem poglavlju osim egzistencije rješenja KdV jednadžbe možemo vidjeti i kako ono izgleda. Također je prikazano solitonsko i dubletsko rješenje iste. U četvrtom poglavlju je dana zanimljiva primjena KdV jednadžbe, njeni razni oblici i njihova rješenja.

Abstract (english)

This diploma thesis presents the existence and a unique solution of the Korteweg-de Vries equation, certain properties and application of the same. The first section of the work defines the canonical form of KdV equation and introduces us through a brief historical sequence to a further development of the KdV equation. The second section introduces the basic concept that will be needed to understand the existence and uniqueness of the KdV equation’s solution. In the third section, apart from the existence of the KdV equation, we can see how it looks. Also presented is a one-soliton and two-soliton solution. The fourth section gives an interesting application of the KdV equation, its various forms and solutions.

• Keywords: Korteweg-de Vries jednadžba; KdV jednadžba; solitonsko rješenje; dubletsko rješenje
• Keywords (english): Korteweg-de Vries equation; KdV equation; one-soliton solution; two-soliton solution
• Language: croatian
• URN:NBN: urn:nbn:hr:217:344276
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2018-05-04 12:12:18