We study a class of sublinear Gardner equations ut+−uα±mumx+uxxx=0, where 0<α<1<m, which exhibit two distinguished features; their solitary waves have a finite span, i.e., are compactons and, depending on their amplitude, may propagate either to the right or to the left, and thus undergo both chase and head-on interactions or, switch direction upon collision. All in all, their morphology, is vastly richer than encountered in the unidirectional KdV-like equations. The multi-dimensional extension ut+−uα±mumx+(∇2u)x=0, reveals an even richer landscape; each admissible velocity supports an entire spectrum of multi-nodal compactons.
|Journal||Communications in Nonlinear Science and Numerical Simulation|
|State||Published - Jul 2022|
- Sublinear Gardner equation