Group invariant solutions of wave propagation in phononic materials based on the reduced micromorphic model via optimal system of Lie subalgebra

Dynamical features and traveling wave structures of the perturbed Fokas-Lenells equation in nonlinear optical fibers

“…This assesment shows the affects of external perturbation force on planar dynamical system's (14) properties. For this, we fix all the other parameters of system (18) and vary the values of ψ and θ. Figures 8 and 9 By using slight adjustments in the magnitude and frequency of the external force, it is possible to demonstrate that a particular model exhibits chaotic behaviour as its solution becomes disordered.…”

“…Several approaches have been suggested, including the improved F-expansion method [7], the variational iteration method [8], the inverse scattering technique [9], the tanh-coth function technique [10], the Jacobi elliptic function expansion technique [11,12] and disciplines, and opened up new avenues. Many of the techniques created for the analysis of NLPDEs exhibit a level of sophistication that makes it challenging for many researchers to access them [14][15][16][17][18]. Today, in many different domains, including plasma physics, optics, biological systems, plasma physics, chemical systems, etc., NLPDEs are ubiquitous and have come to define them [19][20][21][22].…”

“…Figure 11. Sensitivity plot for system(18) with d 1 = − 1, d 3 = 0.003, ψ = 0.05, θ = 0.91 with initial condition (5.1, 0.9) and (5.5, 0.52) for the curves 1 and 2 respectively.…”

Invariance analysis of thermophoretic motion equation depicting the wrinkle propagation in substrate-supported Graphene sheets

“…The balancing index obtained from equation ( 22) is n = 1. Thus, using equation (24), the ansatz for solving equation ( 22) is as follows…”

“…Lie group methods [20][21][22][23][24][25][26][27][28] mainly deal with the nonlinear PDEs to furnish the exact solutions. This technique was initiated by Sophus Lie [29,30] and then followed by Ovsyannikov [31], Ibragimov [32], Bluman [33] and Hydon [34].…”