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Nonlinear Fourier transform - towards the construction of nonlinear Fourier modes
Saksida, Pavle
V članku obravnavamo nelinearno Fourierovo transformacijo, ki je pridružena sistemom tipa ZS-AKNS. Ta verzija nelinearne Fourierove transformacije je primerna za študij nelinearnih analogij ...Fourierovih baz in za perturbacijsko preučevanje nelinearne superpozicije. V članku razvijemo iterativni postopek za izračun inverza naše transformacije. Dobljene formule so izrazljive s pomočjo Bellovih polinomov in njim sorodnih funkcij. V članku dokažemo , da je nelinearna Fourierova transformacija analitična preslikava. To dejstvo zagotavlja konvergenco naše iterativne sheme. Dokažemo, da so člani nelinearnih Fourierovih baz do tretjega reda v perturbacijskem parametru sinusoide, modulirane z drugim Bernoullinevim polinomom. Opišemo uporabo nelinearne superpozicije dveh elementov nelinearne Fourierove baze na problemu prenosa (svetlobe) skozi nelinearen medij.
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