The pseudo-linear superposition principle for nonlinear partial differential equations and representation of their solution by the pseudo-integral

In this paper, for a pseudo-linear partial differential equation of the nth order the pseudo-superposition principle is proved, which means that a pseudo-linear combination of solutions of the equation is again a solution of this equation. Especially, this principle is proved for some equations of the second order imposing weaker conditions. In addition, theorems giving the representation of the solution of Cauchy problem by pseudo-integral are obtained.