Dynamics of quasisolitons in the dispersive
and nonlinear field systems
Yu.S. Gangnus
Saratov State University,
Saratov, Russia
Well known KdV equation is used for description of the waves in the media when nonlinear effects are of important.The spreading of waves in plasma of cold ions and hot electrons and waves on surface of unviscous and noncompressed fluids are described as solutions of the KdV equation.The stability of the solutions comes by means of superposition of nonlinear and dispersion effects in the media when waves are not absorbed. Behaviour of the field systems with the same signs is investigated.
The attemts of description the quantum fields as the dispersive media with the slight nonlinearity are resulted in the equations of motion with the high derivations that has some negative consequences [1]. Earlier we had noted the interesting result of using the high derivations for behaviour of transport coefficients at relativistic temperatures [2]. Now the relativistic analog of KdV equation with high derivations is offered and steady solutions of it are searched. There are some methods of numeral investigation of the same nonlinear problems (for example, [3]). Our aproach is modified method of nets when the reflection of waves from boundary is excepted.
There are a few interesting results. Steady solutions analogous elementary particles with elastic interactions between its are discovered. Its have limited time of life and may be called quasisolitons. There are also solutions disintegrated in two on certain correlations between coefficients of nonlinearity and dispersy. The process may be compared with decay of elementary particles or another nonstable objects.