Fermi resonance solitary wave on the interface between two layers of organic semiconductors

Abstract

The nonlinear dynamics on the interface between two layers of organic semiconductors is discussed for the case of Fermi resonance, which occurs when the excitation energy ប c on one side of the interface approximately equals 2ប b , where ប b is the excitation energy on the other side. In the long wave limit the nonlinear periodic waves can propagate in the form of solitons. A variational approach to the description of such solitary excitations is suggested, which can be applied in a broad range of system parameters.

Approximate solutions and scaling transformations for quadratic solitons

“…Similarly to the two-wave case, the total power P and Hamiltonian H of system (18) can be found for stationary solutions using Eqs. (4,5), where P 0 = P u0 + 2σP w0 + (1/χ)P v0 , H 0 = 0.4[P u0 + αP w0 + (α 1 /χ)P v0 ], and P v0 = +∞ −∞ v 2 0 dx.…”

“…However, the trial functions do not correspond to the actual wave profiles, and thus the "tails", or amplitude asymptotics at x → ±∞, are not described well. In other studies [18], the profiles of the trial functions are chosen as scaled exact solutions ( 6) or (7) with arbitrary amplitudes, but fixed relative widths for the FF and SH wave packets. Due to this limitation, precise results are obtained only for α ≈ 1 and α → ∞ respectively.…”

“…Then, we substitute Eqs. ( 19) into the original system (18) and find a set of coupled equations for the soliton profiles:…”