Abstract

We introduce and study a class of doubly sublinear Gardner equations ut+F(u;n)x+u3x=0 where F(u;n)=u1+n−κ1+2nu1+2n, which for 0<n induce solitons and in the doubly sublinear cases wherein −1/2<n<0, bi-directional compactons propagating in either direction. Their emergence, evolution, chase and head-on interactions are studied.

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