tokens: multilayer system. In general, unlike the symmetric case studied, e.g., by Roberts ( 1981b ), the dispersion relation Equation ( 15 ) cannot be decoupled into two equations that correspond to the well-known sausage (oscillations at the slab boundaries in antiphase, that correspond mathematically to the equation containing ) and kink (perturbations of the slab boundaries oscillating in-phase that correspond to the equation with ) MHD waves. Solutions to Equation ( 15 ) will provide modes modified by the density difference at the sides of the magnetic slab similar to a single asymmetric slab investigated by Allcock Erdélyi ( 2017 ). We adopt the notions of quasi-sausage and quasi-kink to describe these eigenmodes, because they have mixed characters. The slab cross-sectional width, that is constant for symmetric kink modes, is affected for asymmetric kink modes and the line of zero perturbation is shifted for asymmetric sausage modes when compared to the symmetric case, namely, the center of the slab. Furthermore, both the sausage and kink modes can be further categorized as body and surface modes. Surface waves exist when , which corresponds to evanescent solutions of Equation ( 5 ), while body waves exist when , which corresponds to spatially oscillatory solutions. This nomenclature for wave classification was introduced by Roberts ( 1981b ) for symmetric and Allcock Erdélyi ( 2017 ) for asymmetric equilibria. Let us now consider some specific cases of an asymmetric multilayered plasma slab structure that are analytically solvable and have potential for solar application. First, by setting p = q = 0, we verify that the dispersion relation reduces to that which governs the asymmetric slab configuration of Allcock Erdélyi ( 2017 ), namely,We will now focus on cases of two layers (one magnetic and one nonmagnetic), and three (a magnetic layer sandwiched between two nonmagnetic) slabs, respectively, and investigate how the multilayered structure affects the eigenmodes and their eigenfunctions. 2.1 Two-slab Case Let us first consider the case of two slabs, represented by p = 1 and q = 0, which is illustrated by Figure 2 . The width of the nonmagnetic and magnetic slabs are denoted as and d 0 , respectively. Such a model could be useful for modeling MHD waves in MBPs of the solar photosphere (as shown on Figure 3 ). MBPs are approximately vertical magnetic structures between supergranule convection cells of different densities and temperatures. Since neighboring granular cells affect the MBP, we can apply a two-slab description to analyze what will change when comparing eigenmodes to MHD waves in a single slab case. Figure 2. Equilibrium configuration for a two-slab case: a magnetic slab, , and a nonmagnetic slab, . Figure 3. Asymmetric multislab approximation for an elongated MBP, based on Figure 11 of Liu et al. ( 2018 ), observed by the New Vacuum Solar Telescope in TiO 7058 Å. From condition ( 15 ), we obtain the dispersion relationNote, that the
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