On the relations between some well-known methods and the projective Riccati equations


Akçaǧll Ş.

Open Physics, vol.18, no.1, pp.613-618, 2020 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.1515/phys-2020-0124
  • Journal Name: Open Physics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.613-618
  • Keywords: the F-expansion method, the generalized Riccati equation mapping method, the modified Kudryashov method, the projective Riccati equations, the tanh-coth method
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

Solving nonlinear evolution equations is an important issue in the mathematical and physical sciences. Therefore, traditional methods, such as the method of characteristics, are used to solve nonlinear partial differential equations. A general method for determining analytical solutions for partial differential equations has not been found among traditional methods. Due to the development of symbolic computational techniques many alternative methods, such as hyperbolic tangent function methods, have been introduced in the last 50 years. Although all of them were introduced as a new method, some of them are similar to each other. In this study, we examine the following four important methods intensively used in the literature: the tanh-coth method, the modified Kudryashov method, the F-expansion method and the generalized Riccati equation mapping method. The similarities of these methods attracted our attention, and we give a link between the methods and a system of projective Riccati equations. It is possible to derive new solution methods for nonlinear evolution equations by using this connection.