Analytical solutions for nonlinear systems using Nucci's reduction approach and generalized projective Riccati equations-Reference-Cited by-同舟云学术

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

Published:2023 Issue:7 Volume:8 Page:16655-16690
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

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

Reference49 articles.

1. J. G. Liu, W. H. Zhu, L. Zhou, Breather wave solutions for the Kadomtsev-Petviashvili equation with variable coefficients in a fluid based on the variable-coefficient three-wave approach, Math. Methods Appl. Sci., 43 (2020), 458–465. https://doi.org/10.1002/mma.5899

2. J. G. Liu, Q. Ye, Stripe solitons and lump solutions for a generalized Kadomtsev-Petviashvili equation with variable coefficients in fluid mechanics, Nonlinear Dyn., 96 (2019), 23–29. https://doi.org/10.1007/s11071-019-04770-8

3. J. G. Liu, M. S. Osman, Nonlinear dynamics for different nonautonomous wave structures solutions of a 3D variable-coefficient generalized shallow water wave equation, Chin. J. Phys., 77 (2022), 1618–1624. https://doi.org/10.1016/j.cjph.2021.10.026

4. J. G. Liu, A. M. Wazwaz, W. H. Zhu, Solitary and lump waves interaction in variable-coefficient nonlinear evolution equation by a modified ansätz with variable coefficients, J. Appl. Anal. Comput., 12 (2022), 517–532. https://doi.org/10.11948/20210178

5. M. L. Wang, Solitary wave solutions for variant Boussinesq equations, Phys. Lett. A, 199 (1995), 169–172. https://doi.org/10.1016/0375-9601(95)00092-H

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Dynamical investigation of the perturbed Chen–Lee–Liu model with conformable fractional derivative;Zeitschrift für Naturforschung A;2024-08-19

2. Exploring the optical soliton solutions of Heisenberg ferromagnet-type of Akbota equation arising in surface geometry by explicit approach;Optical and Quantum Electronics;2024-05-09

3. Novel kink and multi wave soliton solutions to the stochastic Phi-4 equation driven by the Weiner process;Optical and Quantum Electronics;2024-01-30

4. Three different integration schemes for finding soliton solutions in the (1+1)-dimensional Van der Waals gas system;Results in Physics;2023-12

5. Exact Solutions of Nonlinear Partial Differential Equations Using the Extended Kudryashov Method and Some Properties;Symmetry;2023-11-28