Analytical solutions for nonlinear systems using Nucci's reduction approach and generalized projective Riccati equations

Author:

Yépez-Martínez Huitzilin1,Hashemi Mir Sajjad2,Alshomrani Ali Saleh3,Inc Mustafa45

Affiliation:

1. Universidad Autónoma de la Ciudad de México, Prolongación San Isidro 151, Col. San Lorenzo Tezonco, Del. Iztapalapa, C.P. 09790 México D.F., Mexico

2. Biruni University, Department of Computer Engineering, Istanbul, Turkey

3. Mathematical Modelling and Applied Computation Research Group (MMAC), Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

4. Firat University, Science Faculty, Department of Mathematics, Elazig 23119, Turkey

5. Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Abstract

<abstract><p>In this study, the Nucci's reduction approach and the method of generalized projective Riccati equations (GPREs) were utilized to derive novel analytical solutions for the (1+1)-dimensional classical Boussinesq equations, the generalized reaction Duffing model, and the nonlinear Pochhammer-Chree equation. The nonlinear systems mentioned earlier have been solved using analytical methods, which impose certain limitations on the interaction parameters and the coefficients of the guess solutions. However, in the case of the double sub-equation guess solution, analytic solutions were allowed. The soliton solutions that were obtained through this method display real positive values for the wave phase transformation, which is a novel result in the application of the generalized projective Riccati method. In previous applications of this method, the real positive properties of the solutions were not thoroughly investigated.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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