1. Introduction ................................................. 1
2. Assumptions and preliminaries ................................ 8
3. Weighted Sobolev spaces and regularity of solutions ......... 16
4. The multi-pulse manifold: general structure ................. 25
5. The multi-pulse manifold: projectors and tangent spaces ..... 33
6. The multi-pulse manifold: differential equations and
the cut off procedure ....................................... 40
7. Slow evolution of multi-pulse profiles: linear case ......... 45
8. Slow evolution of multi-pulse structures: center manifold
reduction ................................................... 54
9. Hyperbolicity and stability ................................. 67
10.Multi-pulse evolution equations: asymptotic expansions ...... 74
11.An application: spatio-temporal chaos in periodically
perturbed Swift-Hohenberg equation .......................... 83
Bibliography ................................................... 93
Nomenclature ................................................... 97
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