Asymptotic Approaches to Strongly Non-linear Dynamical Systems

Introduction of small parameters to the real physical problems very often is a delicate and non-trivial problem and may be produced in the various ways. Here we analyze non-linear dynamical equation x + yx + ωx + ðxn = 0 for n → ∞. We propose new formula in the following form x = x0 and this approach is compared with the usual one. We also obtained asymptotic solutions for Eq. (1) for γ = ω 2 = 0, n → ∞; γ = 0, n → ∞. We show that cases ω 2 = 0, n → ∞ and γ ≪⃒ 1, n → ∞ may be reduced to the previous ones.