Exploring solitary waves and nonlinear dynamics in the fractional Chaffee-Infante equation: a study beyond conventional diffusion models. (English) Zbl 07916590
Summary: The current study examines the (2 + 1)-dimensional fractional Chaffee-Infante (FCI) model, which is a nonlinear evolution equation that characterizes the processes of pattern generation, reaction-diffusion, and nonlinear wave propagation. The construction of analytical solutions involves the use of analytical methods, namely the Khater III and improved Kudryashov schemes. The He’s Variational Iteration method is employed as a numerical approach to validate the accuracy of the obtained solutions. The main objective of this study is to get novel analytical and numerical solutions for the FCI model, with the intention of gaining a deeper understanding of the system’s dynamics and its possible implications in the fields of fluid mechanics, plasma physics, and optical fiber communications. The study makes a valuable contribution to the area of nonlinear science via the use of innovative analytical and numerical methodologies in the FCI model. This research enhances our comprehension of pattern creation, reaction-diffusion phenomena, and the propagation of nonlinear waves in diverse physical scenarios.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35Q51 | Soliton equations |
| 76B25 | Solitary waves for incompressible inviscid fluids |
| 78A60 | Lasers, masers, optical bistability, nonlinear optics |
| 35C08 | Soliton solutions |
| 35B36 | Pattern formations in context of PDEs |
| 35R11 | Fractional partial differential equations |
| 65M99 | Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems |
Keywords:
fractional Chaffee-Infante model; nonlinear evolution equation; analytical and numerical solutions; Khater III method; improved Kudryashov method; He’s variational iteration methodReferences:
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