Ag. Walton, ON THE NONEXISTENCE OF PERIODIC NEUTRAL-WAVE SOLUTIONS TO A COMPLEX-VALUED PERIODIC DIFFERENTIAL-EQUATION, Mathematika, 43(86), 1996, pp. 371-381
The equation p ''-lambda'/lambda F(lambda)p'-alpha(2)p=0 where F is a
certain complex-valued function of the given real periodic function la
mbda, is studied analytically and numerically. The equation is motivat
ed physically by a boundary-layer stability problem in which lambda re
presents the skin-friction of the undisturbed basic flow profile. It i
s proved that no periodic neutral solutions exist for any attached bas
ic flow and the implications of this result for certain vortex-wave in
teractions are discussed.