The simplified Hirota’s method for studying three extended higher-order KdV-type equations

In this work we study three extended higher-order KdV-type equations. The Lax-type equation, the Sawada–Kotera-type equation and the CDG-type equation are derived from the extended KdV equation. We use the simplified Hirota’s direct method to derive multiple soliton solutions for each equation. We show that each model gives multiple soliton solutions, where the structures of the obtained solutions differ from the solutions of the canonical form of these equations.