Abstract
The Allen–Cahn equation (ACE), which has applications in solid-state physics, imaging, plasma physics, material science and other fields, is one of the most important models of the modern era for describing the dynamics of oil pollution, reaction-diffusion mechanisms, and the mechanics of crystalline solids. By using the [Formula: see text]-expansion method (GEM) and the Bernoulli sub-ODE schemes, some new traveling wave solutions for the governing model are created in this study (BSODE). The reduced integrable ordinary differential equation is produced using the traveling wave hypothesis. To better understand their behavior, the 3D, contour, and 2D graphs are displayed for a number of fascinating exact solutions. Additionally, we use numerical simulation to confirm the stability of the derived analytical solutions. It results the propagation of temporal soliton for long time of simulation. These results will be used to explain physical phenomenon in crystalline solids and others fields.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
