  We present a study of the wrinkling modes, localized in the plane of single-
and few-layer graphene sheets embedded in or placed on a compliant
compressively strained matrix. We provide the analytical model based on
nonlinear elasticity of the graphene sheet, which shows that the compressive
surface stress results in spatial localization of the extended sinusoidal
wrinkling mode with soliton-like envelope with localization length, decreasing
with the overcritical external strain. The parameters of the extended
sinusoidal wrinkling modes are found from the conditions of anomalous softening
of flexural surface acoustic wave propagating along the graphene sheet in or on
the matrix. For relatively small overcritical external strain, the continuous
transition occurs from the sinusoidal wrinkling modes with soliton-like
envelope to the strongly localized modes with approximately one-period
sinusoidal profiles and amplitude- and external-strain-independent spatial
widths. Two types of graphene wrinkling modes with different symmetry are
described, when the in-plane antisymmetric or symmetric modes are presumably
realized in the graphene sheet embedded in or placed on a compliant strained
matrix. Strongly localized wrinkling modes can be realized without delamination
of the graphene sheet from the compliant matrix and are not equivalent to the
ripplocations in layered solids. Molecular-dynamics modeling confirms the
appearance of sinusoidal wrinkling modes in single- and few-layer graphene
sheets embedded in polyethylene matrix at T = 300K.
