Special decompositions and linear superpositions of nonlinear systems:
BKP and dispersionless BKP equations
Abstract
The existence of decomposition solutions of the well-known nonlinear BKP
hierarchy is analyzed. It is shown that these decompositions provide
simple and interesting relationships between classical integrable
systems and the BKP hierarchy. Further, some special decomposition
solutions display a rare property: they can be linearly superposed. With
the emphasis on the case of the fifth BKP equation, the structure
characteristic having linear superposition solutions is analyzed.
Finally, we obtain similar superposed solutions in the dispersionless
BKP hierarchy.