The aim of this work is to obtain periodic waves of Eq. (1) via ansatz-based methods. So, the open questions are replied and the gap will be filled in the literature…
Abstract
Purpose
The aim of this work is to obtain periodic waves of Eq. (1) via ansatz-based methods. So, the open questions are replied and the gap will be filled in the literature. Additionally, the comparison of the considered models (Eq. (1) and Eq. (2)) due to their performance. Although it is extremely difficult to find the exact wave solutions in Eq. (1) and Eq. (2) without any assumptions, the targeted solutions have been obtained with the chosen method.
Design/methodology/approach
Material science is the today's popular research area. So, the well-known model is the dissipation double dispersive nonlinear equation and, in the literature, open queries have been seen. The aim of this work is to reply open queries by obtaining wave solutions of the dissipation double dispersive model, double dispersive model and double dispersive model for Murnaghan's material via ansatz-based methods.
Findings
The results have been appeared for the first time in this communication work and they may be valuable for developing uses in material science.
Originality/value
The exact wave solutions of Eq. (1) and Eq. (2) without any assumptions have been obtained with via ansatz-based method. So, the open questions are replied and the gap will be filled in the literature.
Details
Keywords
When the literature is reviewed carefully, the analytical solutions of these types of models are missing. First using appropriate similarity transformation, the equations are…
Abstract
Purpose
When the literature is reviewed carefully, the analytical solutions of these types of models are missing. First using appropriate similarity transformation, the equations are reduced to dimensionless form (NODE). To solve the reduced models, ansatz-based methods are considered. Finally, the explicit form solutions are obtained and the effects of material parameters and Prandtl number on the velocity and temperature profiles are shown in figures by the exact solutions. This study aims to discuss the aforementioned solution.
Design/methodology/approach
One of the non-Newtonian fluids is Eyring-Powell (EP) fluid which is derived from the kinetic theory of fluids. Two variations of EP model are considered to obtain the exact solutions that are missing in the literature. In order to obtain exact solutions, one of the ansatz-based methods is considered. The effects of material parameters and Prandtl number on the velocity and temperature profiles are shown in figures by the exact solutions. The results will guide to develop the model to predict the velocity profile and temperature profile when experimental data for dimensionless material parameters of EP fluid are available.
Findings
Finally, the explicit form solutions are obtained and the effects of material parameters and Prandtl number are shown in the figures. The results will guide to develop of the model to predict the velocity profile and temperature profile when experimental data for dimensionless material parameters of EP fluid are available. For the modified EP models, only special cases are considered. The generalized form, i.e. the modified EP models, which include deformation parameters, will be considered in the authors’ future work.
Originality/value
When the literature is reviewed carefully, the analytical solutions of these types of models are missing so by this work, the gap in the literature is filled. The explicit form solutions are obtained and the effects of material parameters and Prandtl number on the velocity and temperature profiles are shown in figures.
Details
Keywords
In the literature, soliton solutions of the Heimburg–Jackson model have been proposed by Drab et al. (2022), but for the considered models, i.e. Eq.(1) and Eq.(2), the existence…
Abstract
Purpose
In the literature, soliton solutions of the Heimburg–Jackson model have been proposed by Drab et al. (2022), but for the considered models, i.e. Eq.(1) and Eq.(2), the existence of solitons, the dispersion analysis and the pseudospectral method have been studied (Engelbrecht et al., 2006, 2018, 2020; Tamm et al., 2017, 2022; Peets et al., 2013). Therefore, the gap should be filled by this work.
Design/methodology/approach
When nonlinear terms, dissipative terms and forcing terms are ignored, the system (Eq.(2)) reduces to a single, sixth-order partial differential equation (Tamm et al., 2022). In this work, our aim is to propose analytical solutions in the explicit form via ansatz-based method. Therefore, the parameter effects in wave profile will be proposed clearly in figures.
Findings
While progress has been made in signal propagation in nerves, thanks to many experimental studies and theoretical predictions over the last two centuries, the results obtained in this study may answer new questions that arise.
Originality/value
In the literature, the existence of solitons, dispersion analysis and pseudospectral method have been investigated for the Heimburg-Jackson model (Engelbrecht et al., 2006, 2018, 2020; Tamm et al., 2017, 2022; Peets et al., 2013), and this study fills the gap in soliton solutions. Additionally, when nonlinear terms, dissipative term and forcing terms are ignored, the system (Eq.(2)) reduced to a single equation that is sixth-order partial differential equation (Tamm et al., 2022). In this work, our aim is to propose analytical solutions in the explicit form via ansatz-based method. Therefore, the parameter effects in wave profile will be proposed clearly in figures.