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| journal = Physics D

| author = L. D. Fadeev, A. A. Slavnov | series = Frontiers in Physics

...ournal = Annales Henri Poincaré. A Journal of Theoretical and Mathematical Physics | MRREVIEWER = Alan D. Rendall

Many equations arising in physics are actually the [[Euler-Lagrange equation]] for some '''variational proble <center><math>\int_{\R^{1+d}} \partial_\alpha f \partial^\alpha f dx dt.</math></center>

Nonlinear wave equations arise in physics from two major sources: relativity and [[elasticity]]. All relativistic field equations in (classical) physics are variants of the [[free wave equation]] or [[Klein-Gordon equation]] on

<center><math>i \partial_t u + \Delta u = f (u, \overline{u}, Du, D \overline{u})</math></center> ...icularly the [[cubic NLS]]) arise as model equations from several areas of physics.

<center><math>\, D=i\eta_{ij}\gamma_i\nabla_j. \!</math></center> ...is a spinor field (solving a coupled massive Dirac equation), and <math>\, D\!</math> is the Dirac operator with connection A. We put <math>y</math> i

| fields = <math>A_\alpha: \R^{1+d} \to \mathfrak{g}</math> | data = <math>A_\alpha[0] \in H^s(\R^d) \times H^{s-1}(\R^d)</math>

...h.caltech.edu/events/mathphys.html 28th annual Western States Mathematical Physics meeting] ....univ-mrs.fr/liste_rencontre/Rencontres2010/Renc353/Renc353.html Équations d'évolution non-linéaires dispersives]

M. Aassilla, ''Nonexistence de solutions globales de certains equations d'ondes nonlineaires'', C. R. Acad. Sci. Paris. '''334''' (2002), 961-966. ...elland, J. Saut, ''Nonlocal models for nonlinear dispersive waves'', Phys. D '''40''' (1989), 360-392.