Anisotropic plasma crystal solitons.

An analytical two-dimensional model for weakly dispersive and weakly nonlinear longitudinal and transverse shear waves propagating in an ideal two-dimensional hexagonal Yukawa crystal is presented. The model takes into account the nonlinear terms up to the third order. Both compressional and shear soliton solutions are found in the long-wavelength approximation. It is shown that the compressional solitons are always supersonic and weakly anisotropic. The shear solitons, on the other hand, exhibit strong anisotropy and can be both subsonic and supersonic, depending on the direction of propagation. In the model, shear solitons cannot propagate along the main axes. The role of weak damping as well as formation of multiple solitons is analyzed. The results are discussed in connection with wave and Mach cone experiments in a monolayer hexagonal plasma crystal, and a diagnostic method is proposed to measure both the charge of the microparticles and the lattice parameter.