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By Liman F.N.

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16. A. T. L. Devaney, Trans. Am. Math. M. Lyapunov, Ann. Fac. Sci. Toulouse, (2) 9, 203, (1907) D. Montgomery and L. Zippin (Interscience, New York, 1955) J. Moser, Coram. Pure and Appl. Math. , 9, 673, (1956) J. Moser, Comm. Pure and Appl. Math. G. W. Quispel, Physics Reports, 2-3 (216), 63, (1992) 17. B. Sevryuk (Springer-Verlag, Berlin, 1986) 18. P. Tokarev, Diff. O. ca ERNESTO PEREZ-CHAVELA Departamento de Matemdticas Universidad Autonoma Metropolitana-Iztapalapa Apdo. mx This is an abstract of a paper, which will be published somwhere else.

The generators of the group Q are spanned by f i , . . ,£q. According to classical Noether theory for symplectic systems, the symplectic flow of a group generates an invariant function. However, in the multisymplectic setting, there is a flow associated with each symplectic structure which generates a family of functions (cf. BRIDGES5). Hence for each generator &, i = 1 , . . , q, there are functionals Fj and Qi such that Mfc(Z) = VPi(Z) and Kfc(Z) = VQi(Z). ,aqt + bqx). Substitution in the multi-symplectic framework (1) shows that the shape Z is a homoclinic or heteroclinic orbit of the Hamiltonian ODE (K - cM)Zx = VV(Z), a p (4) where V(Z) = [S - T,i=i( i i + hQi)]{Z).

15. T. Kapitula and B. Sandstede. Stability of bright solitary-wave solutions to perturbed nonlinear Schrodinger equations. PhysicaD 124:58103, 1998. 16. J. H. Maddocks & R. L. Sachs, On the stability of KdV multi-solitons. Comm. Pure & Appl. Math. 45:867-901, 1993. 17. L. L. Weinstein. Eigenvalues, and instabilities of solitary waves. Phil. Trans. Roy. Soc. Lond. A, 340:47-94,1992. S. L. GANDARIAS AND J. BOX 11510 Puerto Real, Cddiz, Spain. es 40, We apply the Lie-group formalism to deduce symmetries of the generalized Boussinesq equation, utt = « « , , + ( « m + 1 ) _ + 6 [ « ( u ™ ) „ ] u , where a and b are arbitrary constants.

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2-Groups with normal noncyclic subgroups by Liman F.N.


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