Louis De Broglie's An introduction to the study of wave mechanics PDF

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By Louis De Broglie

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I 12 ' (1-44) 2 1 + yo[cos(Kx) + cos(A:y)J"'+ |M| cf. Eqs. 40). As well as the above-mentioned PCF model, the one described by Eq. 44) gives rise to stable 2D solitons, as was first predicted in work [55]. These objects have already been created in the experiment - first, fundamental solitons [66], and then vortical ones [132, 67]. The ID version of Eq. 44), with the expression [cos{kx) + cos{ky)]'^ in the denominator replaced by cos^(/cx), is a physically relevant model too, applying to the propagation of the signal wave through the ID photonic lattice.

Y^ "^^ "-"v^ "* -' / /v ' " - - - ^ \ . ~—'' / ^^^^>z:y/ •"-? ' '^--_ —-' ^''--'. 7: Evolution of the cell-average pulse width in the random-DM system with zero path-average dispersion, as predicted by the variational approximation. The propagation distance exceeds 1000 DM cells. 1. 35), followed by averaging over 200 different realizations of the random length set. To conclude this section, it is relevant to mention that some other versions of the DM systems, also different from strictly periodic ones, were studied too.

02 / ° / T""^ , _ P„-0 , )t, . 5: The peak power of the stable soliton in the DM system vs. the map strength S at different values of the path-average dispersion /3o, as predicted by the variational approximation based on Eq. 29). 4. 6: A counterpart of Fig. 5 obtained from direct numerical simulations of Eq. (2,20). S'cr grows. It is also noteworthy that the value ^max ^ 9-75, predicted by the VA as the stability limit for the DM solitons, is indeed close to what is revealed by direct simulations for small powers, as seen in Fig.

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An introduction to the study of wave mechanics by Louis De Broglie

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