We study the Bäcklund transformations of integrable geometric curve flows in certain geometries. These curve flows include the KdV and Camassa-Holm flows in the two-dimensional centro-equiaffine geometry, the mKdV and modified Camassa-Holm flows in the two-dimensional Euclidean geometry, the Schrödinger and extended Harry-Dym flows in the three-dimensional Euclidean geometry and the Sawada-Kote...

In this paper, the research object is $$(2+1)$$ -dimensional Korteweg–de Vries–Sawada–Kotera–Ramani (KdVSKR) equation. After adding new constraint, solutions which contain y-type molecules are obtained. The process of lump and before after collision studied by long-wave limit method, kinetic behavior analysis given. interactions between resonant soliton molecules, breather obtained combining ve...