Non-propagating solitons of the non-isospectral and variable coefficient modified KdV equation. (English) Zbl 0811.35120
Summary: The AKNS system associated with a non-isospectral and variable coefficient mKdV equation is presented. The method of inverse scattering is adapted to the non-isospectral situation to determine the time evolution of the scattering data. \(N\)-soliton solutions are obtained. Examples of oscillating or standing one-solitons with unusual dynamics are given. An in-depth study of the two-soliton case is carried out by appropriately decomposing the solution into individual soliton elements in order to examine their interactions. Breathers are also constructed.
MSC:
35Q53 | KdV equations (Korteweg-de Vries equations) |
37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
35Q51 | Soliton equations |