## 1 Introduction
In [41], MI was explored by considering the effects of intermodal dispersion, along with higher-order effects, such as the third-order dispersion (TOD) and self-steepening, leading to the conclusion that the intermodal dispersion does not affect the MI growth rate of symmetric or antisymmetric CW states, but can drastically modify the MI of asymmetric CW configurations. Moreover, TOD, as usual, has no influence on the MI gain spectrum in NLDC, while self-steepening can significantly shift the dominant MI band at a sufficiently high input power level. In [42], [PERSON] et al. extended the MI to birefringent fiber couplers by including the cross-phase modulation, polarization mode dispersion, and polarization-dependent coupling. Furthermore, in [43], MI was studied under the combined effects of the intermodal dispersion and saturable nonlinear response. In [44], [PERSON] et al. carried out analytical and numerical investigation of MI for asymmetric CW states in a dissipative NLDC model, based on cubic-quintic complex Ginzburg-Landau equations. In a similar way, in [45], MI was investigated for asymmetric dissipative fiber couplers, which are used in fiber lasers. In that work, the system was asymmetric, as the bar channel was an active (amplified) one, while the cross channel was a passive lossy core (the same setting was investigated as a nonlinear amplifier [46]). In all of the works dealing with the MI, except for [45], it was assumed that the NLDC is completely symmetric with respect to the two cores. Extension of the analysis to asymmetric nonlinear couplers is a subject of obvious interest, as new degrees of freedom introduced by the asymmetry may enhance the functionality of NLDC-based devices [47; 48]. In a simple way, an asymmetric NLDC (ANLDC) can be manufactured using the difference in diameters of the cores, which tends to produce not only the phase-velocity mismatch between them, but also a change in nonlinearity coefficients. Further, the asymmetry can be imposed by deforming transverse shapes of the cores, while maintaining their areas equal. In such birefringent couplers, one can induce a phase-velocity mismatch without a change in the nonlinearity coefficients. Furthermore, to attain the asymmetry, cores with different GVDcoefficients may be used as well. A number of works addressed the switching dynamics [32; 49; 50; 51; 52; 53], stability of solitons [47; 54; 55; 56; 57], logic operations [35; 36], etc., to elucidate possible advantages of the ANLDC over the symmetric couplers. In particular, switching of bright solitons has been studied [49] in the model taking into regard the group- and phase-velocity mismatch and differences in the GVD coefficients and effective mode areas of the two cores. Recently, switching dynamics of dark solitons and interaction dynamics of bright solitons have been investigated in [48; 58]. However, systematic investigation of the MI dynamics and ensuing generation of pulse arrays in ANLDC has not been reported, as of yet. This is the subject of the present work. The remainder of the paper is structured as follows. Section 2 introduces the coupled-mode system for the propagation of electromagnetic fields in the asymmetric coupler. Section 3 presents the linear-stability analysis for the MI induced by small perturbations, followed by further analysis in Section 4. Section 5 reports direct simulations of the nonlinear development of the MI. Section 6 concludes the paper.