Complex structure and solutions of classical nonlinear equation with the interaction $u^4_4$

Details Complex structure and solutions of classical nonlinear equation with the interaction $u^4_4$ Complex structure and solutions of classical nonlinear equation with the interaction $u^4_4$

1996-02-02

arxiv.org/abs/funct-an/9602002v1

Mathematics

Analysis of PDEs

30 pages, LaTeX

Scientific paper

We consider the (real) nonlinear wave equation $$\Box u + m^2 u + \lambda u^3 = 0, \quad m > 0, \quad \lambda > 0, $$ on four-\-dimensional Minkowski space. We introduce the complex structure and show that the (nonlinear) operator of dynamics, the wave and scattering operators define complex analytic maps on the space of initial Cauchy data with finite energy. In other words, let $R(\varphi, \pi) = \varphi + i\mu^{-1}\pi$ be the map of initial data on the positive frequency part of the solution of the free Klein-\-Gordon equation with these initial data. The operators $RU(t)R^{-1},$ $RWR^{-1},$ and $RSR^{-1}$ are defined correctly and are complex analytic on the complex Hilbert space $H^1({\R}^3,\C).$

Affiliated with

Also associated with

No associations

Rating

Complex structure and solutions of classical nonlinear equation with the interaction $u^4_4$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Complex structure and solutions of classical nonlinear equation with the interaction $u^4_4$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Complex structure and solutions of classical nonlinear equation with the interaction $u^4_4$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-597264