Variational Methods in Nonlinear Field Equations by Vieri Benci & Donato Fortunato

Author:Vieri Benci & Donato Fortunato
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(4.44)

Using this notation, we can write Eq. (NKG) in Hamiltonian form:

(4.45)

(4.46)

The time evolution map is defined by

(4.47)

where and is the unique solution of (4.45) and (4.46) satisfying the initial conditions (4.44). The energy and the charge, as functionals defined in X, become

(4.48)

(4.49)

Let

denote the hylenic ratio. We take the following norm in X. If we set

(4.50)

In order to prove the existence of solitons we need the following growth assumption on the function N defined by (4.38) (WC-iii′) There exist such that

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