UDC 519.62, 519.63 Complexes of Localized States in Ac-Driven Nonlinear odinger Equation and in Double Sine-Gordon Equation Schr¨ E. V. Zemlyanaya∗, N. V. Alexeeva†, P. H. Atanasova‡ ∗ Joint Institute for Nuclear Research 6, Joliot-Curie str., Dubna, Moscow region, Russia, 141980 † Department of Math University of Cape Town Rondebosch, South Africa, 7701 ‡ University of Plovdiv “Paisii Hilendarski” FMI, Plovdiv, Bulgaria, 4003 Complexes of localized states are numerically analyzed in two dynamical systems: directly driven nonlinear Schr¨ odinger equation (NLS) and double sine-Gordon equation (2SG). <...> Both systems have a wide range of physical applications. <...> Our numerical approach is based on the numerical continuation with respect to the control parameters of the quiescent (stationary) solutions and stability and bifurcation analysis of the linearized eigenvalue problem. <...> Multisoliton complexes of the NLS equation are studied in the undamped and the weak damping regimes. <...> We show that in the weak damping case the directly driven NLS equation holds stable and unstable multi-soliton complexes. <...> The results are confirmed by means of direct numerical simulations of the time-dependent NLS equation. <...> Properties of the multi-fluxon solutions of 2SG equation are studied depending on the parameter of the second harmonic. <...> We show that the second harmonic changes properties and increases the complexity of coexisting static fluxons of 2SG equation. <...> Results are discussed within the frame of the long Josephson junction model. <...> Introduction nonlinear Schr¨ We study complexes of localized states in two dynamical systems: externally-driven odinger equation (NLS) and double sine-Gordon equation (2SG). wide range of physical applications. <...> In both cases, our numerical approach is based on numerical continuation of staBoth systems have undergone an extensive mathematical analysis because of their tionary solutions of respective partial differential equations and linearized eigenvalue problems [1, 2]. <...> Our aim is a numerical study of (i) multi-soliton complexes of ac-driven NLS in the case of weak damping; (ii) multi-fluxon solutions of 2SG depending on the second harmonic. 2. <...> Complexes in the Ac-Driven, Weakly Damped NLS We consider the nonlinear Schr¨ nal force iψt +ψXX +2|ψ|2ψ −ψ = −h−iγψ, ψX(±∞) = 0, odinger <...>