Quantum and disorder effects in Davydov soliton theory

Within the simple displaced oscillator state ansatz of Davydov [Phys. Scr. 20, 387 (1979)], called the ${\mathit{D}}_2$ ansatz state, the soliton remains stable against strong disorder in the sequences of masses, spring constants, and coupling constants. However, weak diagonal disorder or disorder in the dipole coupling constants destroys the solitons. Within the ${\mathit{D}}_1$ ansatz, in which the quantum nature of the lattice plays a greater role than in the classical ${\mathit{D}}_2$ state, the soliton appears only from nonlinearities roughly 3 to 4 times larger than those in ${\mathit{D}}_2$ models. The sensitivity of such solitons to disorder is practically opposite that for the ${\mathit{D}}_2$ state. Within the partial dressing model we find only dispersing solitary waves, no real traveling solitons. The sensitivity of such waves to disorder is similar to the ${\mathit{D}}_1$ case.