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Lax pairs and Fourier analysis: the case of sine-Gordon and Klein-Gordon equations
Saksida, Pavle
V članku konstruiramo nov Laxov par za Klein-Gordonovo enačbo. Strukturna algebra tega Laxovega para je algebra ▫$\mathcal{TA}_2$▫ zgornje trikotnih Toeplitzevih matrik, ki imajo bloke v algebri ...▫$\mathfrak{su}(2)$▫. Pri primernem izboru vrednosti spektralnega parametra dobimo enostavne izraze za ohranitvene količine, ki jih porodi holonomija prostorskega dela Laxovega para. Ohranitvene količine izrazimo s Fourierovimi podatki enačbe. Integrale Klein-Gordonove enačbe nato primerjamo z ustreznimi integrali sinus-Gordonove enačbe.
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