Comparative Study of Different Discretizations of the $φ^4$ Model

Details Comparative Study of Different Discretizations of the $φ^4$ Model Comparative Study of Different Discretizations of the $φ^4$ Model

2006-08-19

arxiv.org/abs/nlin/0608046v1

Phys.Rev.E76:026601,2007

Nonlinear Sciences

Pattern Formation and Solitons

21 pages, 16 figures. Submitted for publication

Scientific paper

10.1103/PhysRevE.76.026601

We examine various recently proposed discretizations of the well-known $\phi^4$ field theory. We compare and contrast the properties of their fundamental solutions including the nature of their kink-type solitary waves and the spectral properties of the linearization around such waves. We study these features as a function of the lattice spacing $h$, as one deviates from the continuum limit of $h \to 0$. We then proceed to a more ``stringent'' comparison of the models, by discussing the scattering properties of a kink-antikink pair for the different discretizations. These collisions are well-known to possess properties that quite sensitively depend on the initial speed even at the continuum limit. We examine how typical model behaviors are modified in the presence (and as a function) of discreteness and attempt to extract qualitative trends and issue pertinent warnings about some of the surprising resulting properties.

Affiliated with

Also associated with

No associations

Rating

Comparative Study of Different Discretizations of the $φ^4$ Model 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 Comparative Study of Different Discretizations of the $φ^4$ Model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Comparative Study of Different Discretizations of the $φ^4$ Model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-95268