Some new solutions of the Caudrey–Dodd–Gibbon (CDG) equation using the conformable derivative

Advances in Difference Equations

Umar Khan¹  Muhammad Rafiq²  Imran Faisal³  Sadaf Bibi⁴  Naveed Ahmed⁴  Syed Tauseef Mohyud-Din⁴ 

[1] Department of Mathematics and Statistics, Hazara University;Department of Mathematics, COMSATS University Islamabad (CUI);Department of Mathematics, Faculty of Science, Taibah University;Department of Mathematics, Faculty of Sciences, HITEC University;

关键词: Generalized Riccati equation mapping method;    Caudrey–Dodd–Gibbon (CDG) equation;    Soliton solution;    Periodic solution;    Rational solution;    Conformable derivative;   

DOI  :  10.1186/s13662-019-2030-7

来源: DOAJ

【 摘 要 】

Abstract New exact solutions of the space–time conformable Caudrey–Dodd–Gibbon (CDG) equation have been derived by implementing the conformable derivative. The generalized Riccati equation mapping method is applied to figure out twenty-seven forms of exact solutions, which are soliton, rational, and periodic ones. Also, for some suitable values of parameters, the exact solutions are found, namely dark, bell type, periodic, soliton, singular soliton, and several others, by using the conformable derivative. These types of solutions have not been proclaimed so far. 2D and 3D graphical patterns of some solutions are also given for clarification of physical features. The conformable derivative is one of the excellent choices to solve the nonlinear conformable problems arising in theory of solitons and many other areas. The results are new and very interesting for the large community of researchers working in the field of mathematics and mathematical physics.

【 授权许可】

Unknown