A New (4 + 1)-Dimensional Burgers Equation: Its Bäcklund Transformation and Real and Complex N -Kink Solitons

Abstract

Studying the dynamics of solitons in nonlinear evolution equations (NLEEs) has gained considerable interest in the last decades. Accordingly, the search for soliton solutions of NLEEs has been the main topic of many research studies. In the present paper, a new (4 + 1)-dimensional Burgers equation (n4D-BE) is introduced that describes specific dispersive waves in nonlinear sciences. Based on the truncated Painlevé expansion, the Bäcklund transformation of the n4D-BE is firstly extracted, then, its real and complex N-kink solitons are derived using the simplified Hirota method. Furthermore, several ansatz methods are formally adopted to obtain a group of other single-kink soliton solutions of the n4D-BE. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.