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

Abstract

Studying the dynamics of solitons in nonlinear evolution equations (NLEEs) has gainedconsiderable interest in the last decades. Accordingly, the search for soliton solutions ofNLEEs 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 disper-sive waves in nonlinear sciences. Based on the truncated Painlevé expansion, the Bäcklundtransformation of the n4D-BE is firstly extracted, then, its real and complex N-kink solitonsare derived using the simplified Hirota method. Furthermore, several ansatz methods areformally adopted to obtain a group of other single-kink soliton solutions of the n4D-BE