Investigation of Jumps and Solitary Waves in High-Order Dispersion Models

In this paper general principles of research of jumps for nonabsorbing models are considered. Mainly we had investigated wave jumps, described by modified nonlinear Shreodinger equation (NLS) with the third order senior derivative. It was revealed that the boundary conditions on these jumps can be received from three laws of preservation. Numerical investigations of wave interaction with a wall and radiation of a wave in the free space were made. These investigations had confirmed the theoretical assumption that there are jumps with solitary structure and without solitary structure, as well as assumption of existence of three classes of jumps without solitary structure. Comparison to other models, in particular to a modified Korteweg-de-Vries equation was done. The stationary solutions of modified Shreodinger and Korteweg-de-Vries equations, necessary for the analysis of structures of jumps were numerically investigated. The developed methods can be applied to other models also.