2015/12/15 by Sergii Skurativskyi, Skurativskyi, Sergii, V.A. Danylenko +1
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Computational Fluid Dynamics and Aerodynamics #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Pattern Formation and Solitons (nlin.PS)
paper · pdf · doi:10.48550/arxiv.1512.05226
openalex publication_date 2015/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The model we deal with is the mathematical model for mutually penetrating\ncontinua one of which is the carrying medium obeying the wave equation whereas\nthe other one is the oscillating inclusion described by the equation for\noscillators. These equations of motion are closed by the cubic constitutive\nequation for the carrying medium. Studying the wave solutions we reduce this\nmodel to a plane dynamical system of Hamiltonian type. This allows us to derive\nthe relation describing the homoclinic trajectory going through the origin and\nobtain the solitary wave with infinite support. Moreover, there exist a\nlimiting solitary wave with finite support, i.e. compacton. To model the\nsolitary waves dynamics, we construct the three level finite-difference\nnumerical scheme and study its stability. We are interested in the interaction\nof the pair of solitary waves. It turns out that the collisions of solitary\nwaves have non-elastic character but the shapes of waves after collisions are\npreserved.\n