A new (2+1)-dimensional like-Harry-Dym equation with derivation and soliton solutions

Abstract

In this paper, based on the two-dimensional zero-curvature condition, we derived a new ($2+1$)-dimensional nonlinear integrable system, which was subsequently transformed into a ($2+1$)-dimensional Harry-Dym equation. We then established a connection between the corresponding matrix Lax pair and a like KP equation, and obtained 2-soliton solutions via the Darboux transformation. The soliton profiles exhibit distinct knot-like features that highlight the intricate structure of the solutions. Finally, two conservation laws are presented for new equations.