  General higher-order breather and rogue wave (RW) solutions to the
two-component long wave--short wave resonance interaction (2-LSRI) model are
derived via the bilinear Kadomtsev-Petviashvili hierarchy reduction method and
are given in terms of determinants. Under particular parametric conditions, the
breather solutions can reduce to homoclinic orbits, or a mixture of breathers
and homoclinic orbits. There are three families of RW solutions, which
correspond to a simple root, two simple roots, and a double root of an
algebraic equation related to the dimension reduction procedure. The first
family of RW solutions consists of $\frac{N(N+1)}{2}$ bounded fundamental RWs,
the second family is composed of $\frac{N_1(N_1+1)}{2}$ bounded fundamental RWs
coexisting with another $\frac{N_2(N_2+1)}{2}$ fundamental RWs of different
bounded state ($N,N_1,N_2$ being positive integers), while the third one have
${[\widehat{N}_1^2+\widehat{N}_2^2-\widehat{N}_1(\widehat{N}_2-1)]}$
fundamental bounded RWs ($\widehat{N}_1,\widehat{N}_2$ being non-negative
integers). The second family can be regarded as the superpositions of the first
family, while the third family can be the degenerate case of the first family
under particular parameter choices. These diverse RW patterns are illustrated
graphically.
