We present a first-principles derivation of the variational equations describing the dynamics of the interaction of a spatial soliton and a surface plasmon polariton (SPP) propagating along a metal/dielectric interface. The variational ansatz is based on the existence of solutions exhibiting differentiated and spatially resolvable localized soliton and SPP components. These states, referred to as soliplasmons, can be physically understood as bound states of a soliton and a SPP. Their respective dispersion relations permit the existence of a resonant interaction between them, as pointed out in Ref.[1]. The existence of soliplasmon states and their interesting nonlinear resonant behavior has been validated already by full-vector simulations of the nonlinear Maxwells equations, as reported in Ref.[2]. Here, we provide the theoretical demonstration of the nonlinear resonator model previously introduced in our previous work and analyze all the approximations needed to obtain it. We also provide some extensions of the model to improve its applicability.
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