Download PDF by A. Jaffe (Chief Editor): Communications in Mathematical Physics - Volume 193

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K − 1, x0 = −1, xk = x1 + kh. The periodic boundary conditions for the PDE imply that uK (t) ≡ u0 (t). For = 0, system (111) (together with the conjugate equations for u¯˙k ), is Hamiltonian with Hamiltonian H0 = 1 h2 K−1 u¯ k (uk+1 + uk−1 ) − k=1 2 (1 + h2 h ) log(1 + h2 |uk |2 ) , 2 2 (112) and with the symplectic form K−1 ω= k=0 i Im(du¯ k ∧ duk ). 2(1 + h2 |uk |2 ) The discretization (111) gives a tool for approximating solutions of the partial differential Eq. (110), and also offers a finite dimensional model for the phase space structure of the perturbed NLS.

Mech. 29 (3), 367–386 (1994) 39. Tin, S. D. Thesis, Brown University (1994) 40. L. : Non-linear phenomena in forced vibrations of a nearly square plate: Antisymmetric case. J. Sound and Vib. 155, 413–441 (1992) 41. E. : Exact theory of two dimensional self-focusing and one dimensional self-modulation of waves in nonlinear media. Sov. Phys. JETP 34, 62–69 (1972) Communicated by J. L. Lebowitz Commun. Math. Phys. 193, 47 – 67 (1998) Communications in Mathematical Physics c Springer-Verlag 1998 Symplectic Structures on Gauge Theory Nai-Chung Conan Leung School of Mathematics, 127 Vincent Hall, University of Minnesota, Minneapolis, MN 55455, USA Received: 27 February 1996 / Accepted: 7 July 1997 Abstract: We study certain natural differential forms [∗] and their G equivariant extensions on the space of connections.

Math. Anal. (to appear) (1995) 25. Kambe, T. : Nonlinear dynamics of two-mode interactions in parametric excitation of surface waves. J. Fluid. Mech. 212, 373–393 (1990) 26. J. : Multiple-pulse homoclinic orbits near resonance bands. Preprint (1993) 27. Kovaˇciˇc, G. : Orbits homoclinic to resonances, with an application to chaos in the damped and forced Sine-Gordon equation. Physica D 57, 185–225 (1992) 28. Kovaˇciˇc, G. : Homoclinic orbits in the dynamics of resonantly driven coupled pendula.

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Communications in Mathematical Physics - Volume 193 by A. Jaffe (Chief Editor)

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