  A condensed review is presented for two basic topics in the theory of pattern
formation in nonlinear dissipative media: (i) domain walls (DWs, alias grain
boundaries), which appear as transient layers between different states
occupying semi-infinite regions, and (ii) two- and three-dimensional (2D and
3D) quasiperiodic (QP) patterns, which are built as superpositions of
plane-wave modes with incommensurate spatial periodicities. These topics are
selected for the present article, dedicated to the 70th birthday of Professor
M. I. Tribelsky, due to the impact made on them by papers published by Prof.
Tribelsky and his coauthors. Although some findings revealed in those works may
now seem as "old" ones, they keep their significance as fundamentally important
results in the theory of nonlinear DW and QP patterns. Adding to the findings
revealed in the original works by M. I. Tribelsky et al., the present article
also reports several new analytical results, recently obtained as exact
solutions to systems of coupled real Ginzburg-Landau (GL) equations. These are:
a new solution for symmetric DWs in the bimodal system including linear mixing
between its components; a solution for a strongly asymmetric DWs in the case
when the diffusion (second-derivative) term is present only in one GL equation;
a solution for a system of three real GL equations, for the symmetric DW with a
trapped bright soliton in the third component; and an exact solution for DWs
between counter-propagating waves governed by the GL equations with
group-velocity terms. The significance to the "old" and new results collected
in this review is enhanced by the fact that the systems of coupled equations
for two- and multicomponent order parameters, addressed in the article, apply
equally well to modeling thermal convection, multimode light propagation in
nonlinear optics, and binary Bose-Einstein condensates.
