The short envelope soliton dynamics in inhomogeneous dispersive media with allowance for stimulated scattering by damped low-frequency waves

Solitons in an Extended Nonlinear Schrödinger Equation with Pseudo Stimulated Scattering and Inhomogeneous Cubic Nonlinearity

“…For the "initial" condition Ψ(0) = 0, Eq. (18) has the exact solution Ψ(η) = 1 4 cosh η 4Ψ (0) tanh η + tanh η − η + μ μ * (tanh η) ln(cosh η) + 1 12 which is similar to the solutions obtained in [19,23]. For μ = μ * , the solution to Eq.…”

“…For μ = 1/16, the initial pulse numerically tends to the spatially localized distribution with the zero wave number, which is close to the above-obtained analytical solution given by Eq. (19) for α 0 = A 0 = 1 and μ = μ * . If the parameter μ of the pseudo stimulated scattering deviates from the equilibrium value μ * , the numerical simulation shows the nonstationary solitons with the amplitude |U | and the wave number k, which are variable in time t, e.g., for μ = 3/64 = 3μ * /4 (see Figs.…”

“…The soliton class whose existence is caused by the balance of the pseudo stimulated scattering and the inhomogeneous cubic nonlinearity is found. This work is the continuation of [19].…”

“…For μ = μ * , the solution to Eq. (19) satisfies the zero boundary conditions at infinity Ψ(η → ±∞) → 0. This solution exists as a result of balance of the pseudo stimulated scattering and the increasing nonlinearity.…”

“…The model for describing the stimulated scattering of the HF waves from the damped LF waves, which is called pseudo stimulated scattering, is proposed in [17], in which it is shown that the pseudo stimulated scattering shifts the soliton wave-number spectrum to the long-wavelength region. The mechanism of compensation for the pseudo stimulated scattering due to the spatially inhomogeneous dispersion is considered in [17][18][19].…”