  In this paper, we construct a kind of new braided monoidal category over two
Hom-Hopf algerbas $(H,\alpha)$ and $(B,\beta)$ and associate it with two
nonlinear equations. We first introduce the notion of an $(H,B)$-Hom-Long
dimodule and show that the Hom-Long dimodule category $^{B}_{H} \Bbb L$ is an
autonomous category. Second, we prove that the category $^{B}_{H} \Bbb L$ is a
braided monoidal category if $(H,\alpha)$ is quasitriangular and $(B,\beta)$ is
coquasitriangular and get a solution of the quantum Yang-Baxter equation. Also,
we show that the category $^{B}_{H} \Bbb L$ can be viewed as a subcategory of
the Hom-Yetter-Drinfeld category $^{H\o B}_{H\o B} \Bbb {HYD}$. Finally, we
obtain a solution of the Hom-Long equation from the Hom-Long dimodules.
