  Solitons emerge as non-perturbative solutions of non-linear wave equations in
classical and quantum theories. These are non-dispersive and localised packets
of energy-remarkable properties for solutions of non-linear differential
equations. In presence of such objects, the solutions of Dirac equation lead to
the curious phenomenon of "fractional fermion number", a number which under
normal conditions takes strictly integral values. In this article, we describe
this accidental discovery and its manifestation in polyacetylene chains, which
has lead to the development of organic conductors.
