On the lump solutions, breather waves, two-wave solutions of (2+1)-dimensional Pavlov equation and stability analysis

Hirota's bilinear method (HBM) has been successfully applied to the (2+1)-dimensional Pavlov equation to analyze the different wave structures in this paper. The (2 + 1)-dimensional Pavlov equation is used for the study of integrated hydrodynamic chains and Einstein-Weyl manifolds. In our research, we find new solutions in the forms of lump solutions, breather waves, and two-wave solutions. The modulation instability (MI) of the governing model is also discussed. Moreover, a variety of 3D, 2D, and contour profiles are used to illustrate the physical behavior of the reported results. Acquired findings are useful in understanding nonlinear science and its related nonlinear higher-dimensional wave fields. Through the use of Mathematica, the obtained results are verified by inserting them into the governing equation. The strengthening of representative calculations we've made gives us a strong and effective mathematical framework for dealing with the most difficult nonlinear wave problems.