Plohe konstantne negativne zakrivljenosti

master's thesis

• Author: Slavko Davidović
• Mentor: Željka Milin-Šipuš (mentor)
• Committee member: Željka Milin-Šipuš (predsjednik povjerenstva)
• Committee member: Andrej Dujella (član povjerenstva)
• Committee member: Juraj Šiftar (član povjerenstva)
• Committee member: Sanja Varošanec (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2017-02-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu promatrali smo hiperboličke plohe koje pod posebnim uvjetima možemo nazvati pseudosfernim plohama. Veliku ulogu tu je imala Gaussova zakrivljenost za koju smo odredili da bude negativna i konstantna, odakle potječe naslov ovoga rada. Zatim smo izveli sinus-Gordonovu jednadžbu plohe i njenu Bäcklundovu transformaciju koja daje vezu između nove i početne pseudosferne plohe. Na kraju smo vidjeli neke primjere primjena Backlundove transformacije pri generiranju multisolitonskih rješenja.

Abstract (english)

In this thesis we observe hyperbolic surfaces which, under special conditions, are also called pseudospherical surfaces. The crucial part in this case has the Gaussian curvature which we set to be negative and constant. This also gives the title of this thesis. We show that the Bäcklund transformation for the sine-Gordon equation gives connection between new and initial pseudospherical surfaces. Finally, we present some examples of applications of the Bäcklund transformation in construction of multi-soliton solutions.

• Keywords: hiperboličke plohe; pseudosferne plohe; Gaussova zakrivljenost; sinus-Gordonova jednadžba; Bäcklundova transformacija
• Keywords (english): hyperbolic surfaces; pseudospherical surfaces; Gaussian curvature; sine-Gordon equation; Bäcklund transformation
• Language: croatian
• URN:NBN: urn:nbn:hr:217:650207
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2017-04-21 08:48:59