The first results, both positive and negative, recently obtained in the area of constructing stationary spinning solitons in flat Minkowski space in 3+1 dimensions are discussed.

The collision between a kink and a high amplitude breather in the Frenkel-Kontorova chain with a small degree of discreteness was studied numerically and the results were compared with an exact three-soliton solution to the sine-Gordon (SG) equation. It was found that there exists a narrow range of parameters of quasiparticles where the collision in the discrete system is strongly inelastic and...

It is well-known that many dynamical problems in physics and other natural fields are usually characterized by nonlinear evolution partial differential equations known as governing equations. In soliton theory, searching for an analytical exact solution to a nonlinear physical system has long been an important and interesting topic both for physicists and mathematicians since much physical info...

Necessary and sufficient conditions are found for any object in 3+1 dimensions to have integer rather than fractional fermion number. Nontrivial examples include the JackiwRebbi monopole and the already well studied Su-Schrieffer-Heeger soliton, both displaying integer multiples of elementary charges in combinations that normally are forbidden.

based on symbolic manipulation program maple and using riccati equation mapping method several explicit exact solutions including kink, soliton-like, periodic and rational solutions are obtained for (2+1)-dimensional variable coefficient broer--kaup system in quite a straightforward manner. the known solutions of riccati equation are used to construct new solutions for variable coefficient broe...

in this paper, the coupled dispersive (2+1)-dimensional long wave equation is studied. the traveling wave hypothesis yields complexiton solutions. subsequently, the wave equation is studied with power law nonlinearity where the ansatz method is applied to yield solitary wave solutions. the constraint conditions for the existence of solitons naturally fall out of the derivation of the soliton so...