Construction of (n+ 1) -dimensional dual-mode nonlinear equations: multiple shock wave solutions for (3 + 1) -dimensional dual-mode Gardner-type and KdV-type

Abstract

The goal of this study is to offer an exclusive functional conversion to produce (n+ 1) -dimensional dual-mode nonlinear equations. This transformation has been implemented and new (3 + 1) -dimensional dual-mode Gradner-type and KdV-type have been established. Finally, the simplified bilinear method is used to tell the necessary conditions on these new models to have multiple singular-solitons. - 2019, The Author(s).