TY - JOUR
T1 - On the study of double dispersive equation in the Murnaghan's rod
T2 - Dynamics of diversity wave structures
AU - Muhammad, Jan
AU - Younas, Usman
AU - Khan, Aziz
AU - Abdeljawad, Thabet
AU - Almutairi, D. K.
N1 - Publisher Copyright:
© 2024 The Author(s)
PY - 2024/12
Y1 - 2024/12
N2 - This article secures the various wave structures of the fractional double dispersive equation, a significant nonlinear equation that describes the propagation of nonlinear waves within the elastic, uniform, and inhomogeneous Murnaghan's rod. The model under discussion has a wide range of applications in science and engineering. Two recently developed analytical techniques known as the improved generalized Riccati equation mapping method and the multivariate generalized exponential rational integral function method have been applied to the proposed equation for the first time. A variety of solutions have been revealed such that dark, singular, bright-dark, bright, complex, and combined solitons. Furthermore, we include a diverse array of plots that illustrate the physical interpretation of the obtained solutions in relation to a number of significant parameters, thereby highlighting the impact of fractional derivatives. Within the context of the proposed model, these visualizations give a clear understanding of the behavior and characteristics of the solutions. This study's results have the potential to enhance comprehension of the nonlinear dynamic characteristics exhibited by the specified system and validate the efficacy of the implemented techniques. The achieved results significantly enhance our understanding of nonlinear science and the nonlinear wave fields associated with more complex nonlinear models.
AB - This article secures the various wave structures of the fractional double dispersive equation, a significant nonlinear equation that describes the propagation of nonlinear waves within the elastic, uniform, and inhomogeneous Murnaghan's rod. The model under discussion has a wide range of applications in science and engineering. Two recently developed analytical techniques known as the improved generalized Riccati equation mapping method and the multivariate generalized exponential rational integral function method have been applied to the proposed equation for the first time. A variety of solutions have been revealed such that dark, singular, bright-dark, bright, complex, and combined solitons. Furthermore, we include a diverse array of plots that illustrate the physical interpretation of the obtained solutions in relation to a number of significant parameters, thereby highlighting the impact of fractional derivatives. Within the context of the proposed model, these visualizations give a clear understanding of the behavior and characteristics of the solutions. This study's results have the potential to enhance comprehension of the nonlinear dynamic characteristics exhibited by the specified system and validate the efficacy of the implemented techniques. The achieved results significantly enhance our understanding of nonlinear science and the nonlinear wave fields associated with more complex nonlinear models.
KW - Double dispersive equation
KW - Modified generalized Riccati equation mapping method
KW - Multivariate generalized exponential rational integral function method
KW - Solitons
KW - Uniform and inhomogeneous Murnaghan's rod
KW - β-fractional derivatives
UR - http://www.scopus.com/inward/record.url?scp=85205142545&partnerID=8YFLogxK
U2 - 10.1016/j.padiff.2024.100916
DO - 10.1016/j.padiff.2024.100916
M3 - Article
AN - SCOPUS:85205142545
SN - 2666-8181
VL - 12
JO - Partial Differential Equations in Applied Mathematics
JF - Partial Differential Equations in Applied Mathematics
M1 - 100916
ER -