Superposition of soliton, breather and lump waves in a non-painlevé integrabale extension of the Boiti-Leon-Manna-Pempinelli equation

Abstract

In this paper, we derive general $N$th-order Pfaffian solutions for a $(3+1)$-dimensional non-Painlev{'e} integrable extension of the Boiti-Leon-Manna-Pempinelli (BLMP) equation. Specifcally, we obtain $N$-soliton, higher-order breather, higher-order lump and hybrid solutions, and explore the superpositions of Y-shaped and X-shaped soliton-breather waves.
Moreover, we construct bilinear B"{a}cklund transformations, Lax pairs, and conservation laws using Bell polynomials.
Finally, we identify a similar equation in the literature and demonstrate that it represents another non-Painlevé integrable extension of the BLMP equation.