Some properties of slowly decaying oscillatory solutions of KP

In this paper a class of solutions of KP is discussed. Theory of these solutions, referred to here as breathers, is developed and it is shown that a subclass of these solutions can be used to construct more general solutions of KP similarly to how the functions ei(λx+νy) are used to perform the same task in the theory of Fourier transform. Nonlinear superposition formula for general solutions of KP similar to the Fourier expansion formula is considered.