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Taking into account microscopic properties of most usual high-$T_{c}$superconductors, like cuprates, we define a class of microscopic modelHamiltonians for two fermions (electrons or holes) and one boson (bipolaron) onthe two-dimensional square lattice. We establish that these model Hamiltonianscan show d-wave paring at the bottom of their spectrum, despite their spaceisotropy. This phenomenon appear when a "giant electron-phonon anomaly" ispresent at the boundaries of the Brillouin zone ("half breathing"bond-stretching mode), like in doped cuprates. Our results can be used toderive effective electron-electron interactions mediated by bipolarons and wediscuss regimes where the corresponding model is relevant for the physics ofhigh-temperature superconductivity and can be mathematically rigorouslystudied.

d-Wave Pairing Driven by Bipolaric Modes Related to Giant Electron-Phonon Anomalies in High-$T_{c}$ Superconductors