Multi-geometric structures of thermophoretic waves transmission in (2 + 1) dimensional graphene sheets. Stability analysis

Symmetry transformations and novel solutions for the graphene thermophoretic motion equation with variable heat transmission using Lie group analysis

“…The term (kt + α − β) is added to the known KdV equation to be responsible for the acceleration of wrinkles. Another more generalized equation which describes graphene variable heat transmission (vcGT) thermophoretic motion is given by [1,[4][5][6]…”

“…To find different types of solitary wave solutions which could be new and different from other solutions obtained before, we have used the F -expansion technique to solve the reduced equation because that method is stightforward and has many types of solutions. As a result, many Jacobi periodic waves, solitary waves and trigonometric wave solutions were found which are considered new and cover other solutions in the literature [1][2][3][4][5][6][7] since all solutions from eqs. ( 18)-( 31) and ( 37)-( 40) are new and not obtained before but solution (32) is similar to the soliton solution in [4].…”

“…As a result, many Jacobi periodic waves, solitary waves and trigonometric wave solutions were found which are considered new and cover other solutions in the literature [1][2][3][4][5][6][7] since all solutions from eqs. ( 18)-( 31) and ( 37)-( 40) are new and not obtained before but solution (32) is similar to the soliton solution in [4]. Finally, to see the important effect of the variable function a(t) we have chosen three different wave structures to plot it namely, the Jacobi sn, sech, sec waves corresponding to solutions ϑ 1 , ϑ 15 and ϑ 20 , then from the graphs we could see that when a(t) = t, it has a great effect on the propagation shape of the wave, it makes the wave behave like a parabola.…”