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

Abstract

Abstract The goal of this study is to offer an exclusive functional conversion to produce (n+1) $(n+1)$-dimensional dual-mode nonlinear equations. This transformation has been implemented and new (3+1) $(3+1)$-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.

Keywords

• ( 3 + 1 ) $(3+1)$ -dimensional dual-mode Gradner-type
• ( 3 + 1 ) $(3+1)$ -dimensional dual-mode KdV-type
• Simplified bilinear method
• Multiple singular-soliton shock wave solutions