Nonstationary Solitary Wave Numerical Modeling

Problems of applications of numerical methods based on centered approximation of derivatives to modeling of nonstationary behavior of solitary wave-like initial data were discussed in this paper. Especially applications to models with high-order dispassion and dissipation were analyzed. Results of numerical modeling for Korteweg-de-Vries equation, the system of equations of cold quasi-neutral plasma and for Faraday resonance equation for water waves is given. The case, when exact solitary wave solution exists, and the case, when this solution is only the asymptotic one, is investigated. In the letter case the numerical simulating had confirmed theoretical predictions that solitary wave splits with time and illuminates periodic waves with low amplitude. The numerical modeling had showed also that sometimes solitary wave is unstable in spite of existence of exact stationary solitary solution.