Abstract
Abstract Searching for soliton solutions of NPDEs is one of the most interesting and important areas of science in the field of nonlinear phenomena. Soliton is a localized wave with exponential wings or is a localized wave with an infinite support. In this work, we study two extensions of (2+1)-dimensional Boiti-Leon-Manna-Pempinelli (BLMP) equation. Based on the simplified Hirota’s method (HM) and the Cole-Hopf transformation (CHT) method, new multiple front wave solutions are obtained for both versions.