5th International Conference on Theoretical and Applied Physics
Kazan Federal University, Russia
Title: Classification of multidimensional solitary solutions of the GKP equation by use of qualitative and asymptotic analysis
Biography: Vasily Yu Belashov
The problem of classification of the multidimensional nonlinear waves and solitons forming on the low-frequency branch of oscillations in complex continuous media with dispersion, including plasmas and fluids, is studied analytically on the basis of the generalized Kadomtsev-Petviashvili (GKP) equation (as partial case of the Belashov-Karpman (BK) system) which takes into account the generalizations relevant to various complex physical media, associated with the effects of high-order dispersion corrections. To construct the classification of solutions on their types, we consider the dynamical systems associated with the GKP equation and study the structure of these solutions using the methods of qualitative analysis and analysis of the solutions’ asymptotics. We also present some considerations on constructing of the phase portraits of the systems in the 8-dimensional phase space for the GKP equation on the basis of the results of qualitative analysis of the generalized equations of the KdV-class. As a result, we have constructed a classification of possible multidimensional solutions for the GKP system. This is consistent representation of both, the early known and new original results obtained by the author and also some generalizations in theory of the nonlinear waves and solitons in complex dispersive media.