Lax pair, conservation laws and solitons for a (2+12+1)-dimensional fourth-order nonlinear Schrödinger equation governing an αα-helical protein

Energy transfer through a (2+1)-dimensional αα-helical protein can be described by a (2+1)-dimensional fourth-order nonlinear Schrödinger equation. For such an equation, a Lax pair and the infinitely-many conservation laws are derived. Using an auxiliary function and a bilinear formulation, we get the one-, two-, three- and NN-soliton solutions via the Hirota method. The soliton velocity is linearly related to the lattice parameter γγ, while the soliton’ direction and amplitude do not depend on γγ. Interactions between the two solitons are elastic, while those among the three solitons are pairwise elastic. Oblique, head-on and overtaking interactions between the two solitons are displayed. Oblique interaction among the three solitons and interactions among the two parallel solitons and a single one are presented as well.