In this paper, symmetries and symmetry reduction of two higher-dimensional nonlinear evolution equations (NLEEs) are obtained by Lie group method. These NLEEs play an important role in nonlinear sciences. We derive exact solutions to these NLEEs via the $\exp(-\phi (z))$ -expansion method and complex method. Five types of explicit function solutions are constructed, which are rational, exponential, trigonometric, hyperbolic and elliptic function solutions of the variables in the considered equations.

In this article, we introduce two recent results with respect to the integrality and exact solutions of the Fisher type equations and their applications. We obtain the sufficient and necessary conditions of integrable and general meromorphic solutions of these equations by the complex method. Our results are of the corresponding improvements obtained by many authors. All traveling wave exact solutions of many nonlinear partial differential equations are obtained by making use of our results. Our results show that the complex method provides a powerful mathematical tool for solving a great number of nonlinear partial differential equations in mathematical physics. We will propose four analogue problems and expect that the answer is positive, at last. MSC:30D35, 34A05.

In this article, with the aid of Maple software, the exact solutions to the space-time fractional symmetric regularized long wave (SRLW) equation are successfully examined by G ′ / G 2 -expansion and extended complex methods. Consequently, three types of traveling wave solutions are found such as Weierstrass double periodic elliptic functions, simply periodic functions, and the rational function solutions. The obtained results will play an important role in understanding and studying SRLW equation. It is easy to see that the extended complex and G ′ / G 2 -expansion methods are reliable and will be used extensively to seek exact solutions of any other fractional nonlinear partial differential equations (FNPDE).