  A method is presented to construct exactly solvable nonlinear extensions of
the Schr\"odinger equation. The method explores a correspondence which can be
established under certain conditions between exactly solvable ordinary
Schr\"odinger equations and exactly solvable nonlinear theories. We provide
several examples illustrating the method. We rederive well-known soliton
solutions and find new exactly solvable nonlinear theories in various space
dimensions which, to the best of our knowledge, have not yet been discussed in
literature. Our method can be used to construct further nonlinear theories and
generalized to relativistic soliton theories, and may have many applications.
