Exact Solutions of Non-Conservative Equations for Three-Wave and Second- Harmonic Resonance

New solutions of the equations of three-wave and second-harmonic resonance are presented, in cases where these equations are non-conservative. With three waves subject to both finite linear damping and complex coupling coefficients, these new solutions depend on a single characteristic variable. In the absence of linear damping, but with complex coupling coefficients, a broad class of solutions depending on three characteristic variables is found. This class is a generalization of the so-called 'one-lump' solutions previously known only for conservative equations with real coupling coefficients. For second-harmonic reasonance, analogous new solutions are given for both conservative and non-conservative cases.