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Example text
Nevertheless in this case there exists such a set of values iB . H . = e 1k/2, P 1 k > j 2 1, that define the "interaction' 0 s the components L Ik with different phases of the solution Y ~ ( T ~ ~ . . , T ~For ) . 12) by solving which with respect to V following relations: G = 9 (UIH,C) , H . 20) $jk(U,H,C)r. ]=1,2, k=2 ' where f i = (Hll,H12),U = (U ,U ) and $ and 0 are functions. 15) and it is naturally to call them the multidimensional dispersion relations. Distinct from one-dimensional case ( V .
A292, N 1430 (1966) 403-412. , Operational methods ("PTIR", Moscow, 1976). 1141 Maslov V . P . , Complex WKB-method in non-linear equations ("Nauka", Moscow, 1977) (in Russian). El51 Maslov V . P . , &-like generalized according to Sobolev solutions of quasi-linear equations, Uspekhi Math. Nauk 34, N1 (1979) 235-236 (in Russian). , Abelian functions and solutions, Inst. Theor. , Univ. Wroclaw, Preprint N 373, 1976. , Application of non-linear WKB-method to KdV equation, SIAM Appl. Math. 26, N2 (1974) 376-395.
Symmetric spaces of negative curvature. The most fruitful approach to the analysis of symmetric spaces is via group theory. S o for us a negatively curved symmetric space S is a space on which a noncompact connected semisimple Lie group G acts transitively and such that the stabilizer of a point of S is a maximal compact subgroup K of G. That is, S may be identified with K\G and the space of functions (resp. distributions) on S with the space of left K-invariant functions (resp. distributions) on G.