Abstract
In this article, the exact solutions to the potential Yu–Toda–Sasa–Fukuyama equation are successfully examined by the extended complex method and (G′/G)‐expansion method. Consequently, we find solutions for three models of Weierstrass elliptic functions, simply periodic functions, and rational function solutions. The obtained results will play an important role in understanding and studying potential Yu–Toda–Sasa–Fukuyama equation. It is observed that the extended complex method and (G′/G)‐expansion method are reliable and will be used extensively to seek for exact solutions of any other nonlinear partial differential equations (NPDEs).
Highlights
As is known to all, the development of modern natural science is linear
The application of nonlinear science in power systems has become more and more extensive. It provides a large number of reliable references for the operation and planning of the power system. e application of nonlinear equations promoted the development of nonlinear sensitive electronic devices on the load side and grid side of the power system. e stable operation of power system at each level can be effectually protected by exploring the nonlinear phenomena in the case of ferromagnetic resonance overvoltage situation. e harmonic linearization method is proposed to solve the asymmetric nonlinear oscillation problem in the parallel operation of power stations, which will help to select the grid structure reasonably and effectively improve the stability of the grid structure [2]. e high-frequency disturbances that may be encountered can be predicted by constructing a nonlinear prediction model with random disturbances [3]
The complex method and (G′/G)− expansion method are employed by us to seek for the exact solution of (4). ese two methods will play a significant role in constructing exact solutions for the nonlinear partial differential equations via the (3 + 1)− dimensional potential-YTSF equation
Summary
As is known to all, the development of modern natural science is linear. Nonlinear science is considered as the most essential forefront of the fundamental understanding of nature. The application of nonlinear science in power systems has become more and more extensive. There are many effective and magical methods to obtain exact solutions of nonlinear differential equations, such as Backlund transformation method [8], continuation method [9], Painlevetruncation extension method [10, 11], Hirota bilinear method [12, 13], Exp(− φ(z))-Expansion method [14, 15], and so on. In 2019, Zhao and He [20] employed the bilinear method to study the (3 + 1)− dimensional potential-YTSF equation in fluid dynamics. Ese two methods will play a significant role in constructing exact solutions for the nonlinear partial differential equations via the (3 + 1)− dimensional potential-YTSF equation The complex method and (G′/G)− expansion method are employed by us to seek for the exact solution of (4). ese two methods will play a significant role in constructing exact solutions for the nonlinear partial differential equations via the (3 + 1)− dimensional potential-YTSF equation
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