TY - JOUR
T1 - Dynamical structures of wave front to the fractional generalized equal width-Burgers model via two analytic schemes
T2 - Effects of parameters and fractionality
AU - Pervin, Mst Razia
AU - Harun-Or-Roshid,
AU - Abdeljabbar, Alrazi
AU - Dey, Pinakee
AU - Shanta, Shewli Shamim
N1 - Publisher Copyright:
© 2023 the author(s), published by De Gruyter.
PY - 2023/1/1
Y1 - 2023/1/1
N2 - This work focuses on the fractional general equal width-Burger model, which describes one-dimensional wave transmission in nonlinear Kerr media with combined dispersive and dissipative effects. The unified and a novel form of the modified Kudryashov approaches are employed in this study to investigate various analytical wave solutions of the model, considering different powers of nonlinearity in the Kerr media. As a result, a wide range of structural solutions, including trigonometric, hyperbolic, rational, and logarithmic functions, are formulated. The achieved solutions present a kink wave, a collision of kink and periodic peaked soliton, exponentially increasing wave profiles, and shock with a dark peaked wave. The obtained solutions are numerically demonstrated for specific parameter values and general parametric powers of nonlinearity. We analyzed the effect of existing parameters on the obtained wave solutions with numerical graphics. Moreover, the stability of the model is analyzed with a perturbed system. Furthermore, a comparison with published results in the literature is provided, highlighting the differences and similarities. The achieved results showcase the diversity of structural solutions obtained through the proposed approaches.
AB - This work focuses on the fractional general equal width-Burger model, which describes one-dimensional wave transmission in nonlinear Kerr media with combined dispersive and dissipative effects. The unified and a novel form of the modified Kudryashov approaches are employed in this study to investigate various analytical wave solutions of the model, considering different powers of nonlinearity in the Kerr media. As a result, a wide range of structural solutions, including trigonometric, hyperbolic, rational, and logarithmic functions, are formulated. The achieved solutions present a kink wave, a collision of kink and periodic peaked soliton, exponentially increasing wave profiles, and shock with a dark peaked wave. The obtained solutions are numerically demonstrated for specific parameter values and general parametric powers of nonlinearity. We analyzed the effect of existing parameters on the obtained wave solutions with numerical graphics. Moreover, the stability of the model is analyzed with a perturbed system. Furthermore, a comparison with published results in the literature is provided, highlighting the differences and similarities. The achieved results showcase the diversity of structural solutions obtained through the proposed approaches.
KW - dispersive effects
KW - dissipative effects.
KW - fractional GEW-Burger model
KW - Jumarie's Riemann-Liouville derivative
KW - Kerr media
KW - unified scheme
UR - http://www.scopus.com/inward/record.url?scp=85175788986&partnerID=8YFLogxK
U2 - 10.1515/nleng-2022-0328
DO - 10.1515/nleng-2022-0328
M3 - Article
AN - SCOPUS:85175788986
SN - 2192-8010
VL - 12
JO - Nonlinear Engineering
JF - Nonlinear Engineering
IS - 1
M1 - 20220328
ER -