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...

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...

Extending the gauge-invariance principle for τ functions of the standard bilinear formalism to the supersymmetric case, we define N=1 supersymmetric Hirota operators. Using them, we bilinearize SUSY KdV-type equations (KdV, Sawada-Kotera-Ramani, Hirota-Satsuma). The solutions for multiple collisions of super-solitons and extension to SUSY sine-Gordon are also discussed.

We consider the solution of spectral problems with elliptic potentials in the framework of the Hermite ansatz. We show that the search for potentials and their spectral characteristics is reduced to a system of polynomial equations solvable by the Gröbner bases method and others. New potentials and corresponding solutions of the Sawada–Kotera, Kaup–Kupershmidt, Boussinesq equations are found.