Electronic Journal of Differential Equations, Vol. 2021 (2021), No. 41, pp. 1-14.

Title: Lie symmetry analysis and conservation laws for the (2+1)-dimensional Mikhalev equation
       
Authors: Xinyue Li (Shandong Univ. of Science and Tech., Qingdao, China)
         Yongli Zhang (Qingdao Univ., Qingdao, Shandong, China)
         Huiqun Zhang (Qingdao Univ., Qingdao, Shandong, China) 
         Qiulan Zhao (Shandong Univ. of Science and Tech., Qingdao, China)

Abstract: 
 Lie symmetry analysis is applied to the (2+1)-dimensional Mikhal\"ev equation,
 which can be reduced to several (1+1)-dimensional partial differential equations with
 constant coefficients or variable coefficients. Then we construct exact explicit solutions
 for part of the above (1+1)-dimensional partial differential equations. Finally,
 the conservation laws for the (2+1)-dimensional Mikhal\"ev equation are constructed
 by means of Ibragimov's method.

Submitted October 28, 2020. Published May 07, 2021.
Math Subject Classifications: 35Q53, 37K30;,37K40.
Key Words: (2+1)-dimensional Mikhalev equation; Lie symmetry analysis;
           similarity reduction; conservation law; exact solution.