Generalized bilinear Backlund transformation: a novel approach to find exact solutions

This study presents a novel approach to the generalized bilinear Backlund transformation, motivated by recent developments of generalized exchange identities. Generalized bilinear Backlund transformation combines the derivation of separate bilinear Backlund transformations with different exchange identities into a single formulation. This formulation provides a more comprehensive approach to analyze nonlinear integrable systems, as it includes a wider range of free parameters and multiple transformation relations that generate various exact solutions and wave patterns. To demonstrate the method, the (3 + 1)-dimensional Jimbo-Miwa equation is considered and this generalized bilinear Backlund transformation formulation highlights the effectiveness and applicability of the approach through illustrative examples.