A Schrödinger equation is examined which describes the motion of superfluid condenste in thin 4He films. The equation includes full nonlinearity arising from the van der Waals potential due to substrate. In contrast to the ordinary nonlinear Schrödinger equation (|ψ|2ψ type) which has been solved by inverse-scattering method, it is extremely difficult to apply such analytic method to our equation. Numerical study shows, however, that there indeed exist, in our system, solitons which have asymmetric shape, and are quite stable through collisions with each other and with fixed boundary walls. Thus the present work generalizes KdV-soliton theories for 4He films to the fully nonlinear case.