On the Painlevé integrability of three-extensions to Mikhailov–Novikov–Wang equations: Multiple solitons, shocks, and other physical solutions

Abstract

The current work examines three (1 + 1)-dimensional Mikhailov–Novikov–Wang (MNW) equations. The Painlevé criteria are employed for testing the integrability of the evolution equations. Using the simplified Hirota's approach, multiple soliton solutions for the family of the MNW equation are derived. Significant physical solutions, such as shock waves, periodic solutions, and many others, are also obtained for each equation under consideration. The current investigation provides insights into the integrability features of these evolution equations. The obtained outcomes will contribute to comprehending and studying many enigmatic phenomena that consistently manifest in nature and various nonlinear media, including optical fiber, fluid mechanics, and plasma physics.