i.e. they could be easily driven by external fields, and they may thus significantly contribute to the dielectric or piezoelectric response of the material. For several temperatures, we have numerically investi- gated domain walls allowing for more complicated CPP solutions with non-constant P$_{t}$ . We have identified solu- tions, which could be considered as analogues of Bloch walls known from magnetism. Interestingly, in contrast with Ref. 3, our model predicts the Ising-type profile of the O180 { 1 ¯ 10 } wall. At the same time the Bloch-like structure of the O180 { 001 } wall is predicted. We believe that this kind of somewhat exotic walls ac- tually represent important generic examples of ferroelec- tric domain species, which should be anticipated in all ferroelectrics with several equivalent domain states dis- tinguished simultaneously by the orientation of the spon- taneous polarization and strain. They should be certainly taken into account in investigations of domain-wall phe- nomena in ferroelectric perovskites. At the same time, the energy differences between the Bloch-like and Ising- like solutions are rather subtle here. Therefore, in spite of the fairly good agreement for 180 ◦ and 90 ◦ domain walls between ab-initio calculations and predictions of this model in the tetragonal phase, 4 the preference for the calculated Bloch-like trajectories may not necessar- ily reproduced for the domain walls encountered in real BaTiO$_{3}$ crystal, since there is obviously a considerable uncertainty in the adopted material-specific GLD param- eters. In addition, predictions for the domain walls with very small thickness must be considered with a particu- lar caution since the description of the sharp domain wall profiles obviously touches the limits of the applicability of the continuous model. In conclusion, we have derived a number of qualita- tive and quantitative predictions for mechanically com- patible neutral domain walls of tetragonal, orthorhombic and rhombohedral BaTiO$_{3}$ on the basis of the previously proposed material-specific GLD model. We believe that the insight into the domain wall properties mediated by the provided analytical and numerical analysis could be helpful for understanding of domain wall phenomena in BaTiO$_{3}$ as well as in some other intensively investigated members of the ferroelectric perovskite family with same sort of macroscopic ferroelectric phases, for example in KNbO$_{3}$, BiFeO$_{3}$, PbTiO$_{3}$ or even PZT and perovskite relaxor-related materials. The work reports detailed study of mechanically com- patible and electrically neutral domain walls in BaTiO$_{3}$. The investigation was done within the framework of the GLD model. Using the SPP approximation it was possi- ble to compare properties of various kinds of domain wall species from the same perspective. The phenomenological nature of the GLD model al- lowed to predict the temperature dependence of the do- main wall characteristics in the whole temperature range of ferroelectric phases. Its continuous nature gave us even the opportunity to deal conveniently with the non- crystallographic S-type domain wall, which has a general orientation with respect to the crystal lattice, and which is therefore difficult to cope with in discrete models rely- ing on periodic boundary conditions. The S-wall in the orthorhombic, as well as the 90 wall in tetragonal phase were both found to be about 4 nm thick and consequently are expected to be mobile, Authors are grateful to Prof. V. Janovec for helpful comments and critical reading of the manuscript. The work has been supported by the Czech Science Founda- tion (Projects Nos. P204/10/0616 and 202/09/0430). Acknowledgments VII. CONCLUSION FIG. 9: Profiles of polarization components in R180 { 1 ¯ 10 } domain wall showing the SPP stationary trajectory (a) as well as the lower energy Bloch-like solution (b), both for the model parameters corresponding to T = 118 K. Full line stands for the P$_{r}$ component of polarization vector, broken line for the P$_{t}$ one. The bottom panel demonstrates that Bloch solution may considerable modify the domain domain wall profile. 11