Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2012-03-16
Nonlinear Sciences
Pattern Formation and Solitons
15 pages, 10 figures
Scientific paper
A higher-order dispersive equation is introduced as a candidate for the governing equation of a field theory. A new class of solutions of the three-dimensional field equation are considered, which are not localized functions in the sense of the integrability of the square of the profile over an infinite domain. For the new type of solutions, the gradient and/or the Hessian/Laplacian are square integrable. In the linear limiting case, analytical expression for the pseudolocalized solution is found and the method of variational approximation is applied to find the dynamics of the centers of the quasi-particles (QPs) corresponding to these solutions. A discrete Lagrangian can be derived due to the localization of the gradient and the Laplacian of the profile. The equations of motion of the QPs are derived from the discrete Lagrangian. The pseudomass ("wave mass") of a QP is defined as well as the potential of interaction. The most important trait of the new QPs is that at large distances, the force of attraction is proportional to the inverse square of the distance between the QPs. This can be considered analogous to the gravitational force in classical mechanics.
Christov Christo I.
No associations
LandOfFree
Pseudolocalized Three-dimensional Solitary Waves as Quasi-Particles 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 Pseudolocalized Three-dimensional Solitary Waves as Quasi-Particles, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Pseudolocalized Three-dimensional Solitary Waves as Quasi-Particles will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-352444