Exact Solutions and Conservation Laws of the Bogoyavlenskii Equation

Mathematical modelling of scientific events is illustrated by nonlinear evolution equations (NLEEs). As such, it is important to obtain the general solutions of these models. The solutions of nonlinear partial differential equations (NLPDE’s) provide a lot of information related to the character and structure of nonlinear models to researchers [1]. Many efficient techniques have been enhanced to provide useful information for researchers in the field of mathematics, physics and engineering. During the last decades, a variety of techniques have been recommended to analyze the behavior of NLPDEs [2–34]. Lie’s classical theory is a basic of some generalizations. One of these generalizations is presented as a nonclassical approach by Bluman and Cole [3]. The most convenient description of Lie’s invariance for initial value problems (IVPs) is given and summarized by Bluman et al. [4, 5]. Details of the Lie symmetry technique is given in [6]. A technique for investigating the special symmetries of NLPDEs can also be found in [7]. In this paper, we will consider the Bogoyavlenskii (BK) equation given by [9–11]: { aut + uxxy + bu uy + Cuxυ = 0, uuy − υx = 0, (1)