The anisotropy of metal crystal surfaces is known to affect the dynamics of travelling concentration wavetrains (including front- and pulse-like waves) observed in heterogeneous catalytic reactions. Motivated by experiments on microdesigned catalyst surfaces we present a computer-assisted study on the stability of pulse-like solutions of reaction-diffusion equations in thin (quasi-one-dimensional) anisotropic media. Results on a period doubling instability of a rotating pulse and on the interaction of two pulses in a system with periodic boundaries are reported.