A method is developed which generates a class of nonlinear evolution equations in two and three spatial dimensions from an associated eigenvalue problem and its time dependence. Special cases include the equations describing nonlinear, resonantly interacting, wave envelopes in two and three dimensions; a "nonlinear Schrödinger" equation in two dimensions; and a two-dimensional analog of the Korteweg- de Vries equation.

• Received 25 June 1975

DOI:https://doi.org/10.1103/PhysRevLett.35.1185