Existence of solutions and generalized solutions in one-dimensional nonlinear equations

One dimensional translation-invariant equations are studied, in particular, the one-dimensional non-linear equations of Schroedinger i(delta psi (x,t)/delta t=-(delta2 psi (x,t))/delta x2+Z integral Z (W(x-y) psi (x,t) abs(psi(y,t))2dy) and the equation delta2 phi/delta t2 - delta2 phi/delta x2 - lambda phi+Z integral Z(W(x-y) phi(x,t) phi2 (y,t)dy)=0. The existence of particle-like solutions of these equations is proved