Multitime KdV solitons

The term of multitime soliton has recently been coined in our research school to describe a multitime pulselike nonlinear wave (multitime solitary wave) which emerges from a collision with a similar pulse having unchanged shape and speed vector. To introduce this notion, it was necessary to introduce multitime PDEs that extend solitonic single-time PDEs via geometrical ingredients. This paper covers the status for multitime soliton research based on multitime dual power law nonlinear KdV PDE, paying particular attention to methods whereby an initial value problem for such a PDE can be solved exactly through a succession of calculations. Discussion of the interaction between two bi-temporal solitons show their own physical sense. M.S.C. 2010: 37K40, 35C08, 35Q51.