# Nonlinear theory of localized and periodic waves in solids undergoing major rearrangements of their crystalline structure

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This paper shows how to solve some nonlinear wave equations as perturbation expansions in powers of a parameter that expresses the degree of nonlinearity. For the case of the Burgers equation ut+uux=uxx, the general nonlinear equation ut+uÎ´ux=uxx is considered and expanded in powers of Î´....

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The pair force interaction potential that allows one to describe a deviation from spherical symmetry, which is typical for hexagonal close-packed structures, is constructed using the 'spherically symmetric' Mie potential that depends only on the interatomic distance. The parameters of the...

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- Manifestation of quasi-symmetry of the cation sites of Gd[sub 2]SiO[sub 5], Y[sub 2]SiO[sub 5], and Lu[sub 2]SiO[sub 5] in the spectra of the impurity ion Pr[sup 3+]. Malyukin, Yu. V.; Borisov, R. S.; Zhmurin, P. N.; Lebedenko, A. N.; Grinev, B. V.; Znamensky, N. V.; Manykin, E´. A.; Orlov, Yu. V.; Petrenko, E. A.; Yukina, T. G. // Low Temperature Physics;Jul2001, Vol. 27 Issue 7
The quasi-symmetry of the inequivalent cation sites in the crystals Gd[sub 2]SiO[sub 5], Y[sub 2]SiO[sub 5], and Lu[sub 2]SiO[sub 5] is established on the basis of an analysis of the features of the low-temperature optical spectra of the impurity ion Pr[sup 3+]. One type of cation site of the...

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Nonlinear evolution equation (NLEE) systems model the most essential topics in nonlinear sciences. Exact solutions of these equations play a major role in the suitable understanding of mechanisms of the various physical phenomena modelled by these NLEEs. For this reason, searching exact...