New symmetries and their Lie algebra properties for the Burgers equations

Wave interactions and the analysis of the perturbed Burgers equation

“…As we shall use the symmetries of the Burgers equation repeatedly, we summarize their properties [16][17][18] in brief. The symmetries, S n , are solutions of the linearization of the Burgers equation…”

Two-component description of dynamical systems that can be approximated by solitons: The case of the ion acoustic wave equations of plasma physics

“…The equation that determines u (n) , the n th -order correction in the solution of the PKDVE is Eq. (A.2) has an infinite hierarchy of solutions [3][4][5][6][7][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56], the symmetries of the KdV equation.…”

“…Eq. (A.2) has an infinite hierarchy of solutions [3][4][5][6][7][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56], the symmetries of the KdV equation.…”

Spontaneously generated waves in perturbed evolution equations

“…In the case of the Burgers equation, the multiple-front solution is constructed from exponential waves that are solutions of the diffusion equation [22][23][24]. Focusing on front solutions that vanish in some direction in the x-t plane, we show that, again, the obstacle to integrability represents coupling between such fronts and other wave fronts.…”

“…In the following, we shall need S n , the symmetries of the Burgers equation, as well as their spatial integrals, G n [22][23][24]. In a first-order analysis, the first three symmetries are needed:…”