However a more technologically driven reason is that domain walls present in ferromagnetic substances are widely used for the storage of data. The internal structure of static domain wall systems has been successfully described using a classical continuum model. One such approach involves using a functional to describe the energy of a static domain wall, in a manner completely analogous to defining a Lagrangian for a mechanical system. The structure of the wall can then be determined by minimizing this energy according to Hamilton's principal. This balance between the two energies is the hallmark characteristic of a soliton solution.
Solitons are well known exact solutions to nonlinear integrable systems.
It is perhaps not surprising that it is possible to obtain analytic expressions, mostly in terms of elliptic, trigonometric, and hyperbolic functions, for many one dimensional domain wall systems.