Integral invariants and complex eigenvalue bounds (Q1117375)

Many areas in classical applied mathematics and mathematical physics generate systems of partial differential equations that describe wave propagation and/or stability to perturbations about a stable equilibrium. Very often the linearized equations are susceptible to integral transformation and a reduced system of ordinary differential equations with complex coefficients may be obtained. In this note a straightforward method is established for reducing two coupled equations of this type to a system that can be easily manipulated mathematically while retaining physical significance. Eigenvalue bounds are often more readily accessible under these circumstances. Brief examples are provided from the study of shear-magnetoacoustic-gravity (SMAG) waves.