1 Universidad de Caldas, Calle 65 No. 26-10, P.O. Box: Apartado Aéreo 275, Manizales, Caldas, Colombia 2 Department of Mathematics, Universidad Nacional de Colombia, Carrera 27 No. 64-60, P.O. Box: Apartado Aéreo 275, Manizales, Colombia 3 Department of Mathematics, Universidad Nacional de Colombia, Calle 45, Carrera 30. P.O. Box: Apartado Aéreo 52465, Bogota, Colombia 4 Department of Mathemati...

This article uses the Yang transform decomposition method and homotopy perturbation to study seventh-order time-fractional Sawada–Kotera–Ito equation. The fractional derivative is taken into account in Caputo sense. We used with Adomian process procedure on problem obtain solution. looked at a single case contrasted it actual result validate methodologies. These techniques create recurrence rel...

Based on the N-soliton solutions of $$(2+1)$$ -dimensional Sawada–Kotera equation, collisions among lump waves, line and breather waves are studied in this paper. By introducing new constraints, wave does not collide with other forever, or stays collision forever. Under condition velocity resonance, soliton molecules consisting a wave, any number derived for first time. In particular, interacti...

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.