[Linear and Nonlinear Waves, Whitham (1974), p. 96, Chapter 4. Burgers' equation] a Prerequisite: a The simplest equation combining both nonlinear propagation eects and diffusive effects in Burgers' equation 0 ct + ccx = VCxx.-= (4.1).: a 0 This is an exact equation for waves described by +- p: +qx = 0, q = (2(9) _Vpxt' (42E 0 In the case that Q(p) is a quadratic mction of p. In general, if the two effects are important in a problem, there is usually some way of extracting (4.1) either as a precise approximation 01' as a use.11 basis for rough estimates. 9 For a general Q(p) in (4.2), for example, the equation may be writtenu ct + cox = vcxx vc\"(p)px2,o (43%\" .3 Where C(p) = Q'(p) as usual..: Question: .J Show that the ratio of vc\"(p)px2 to vent in the right-hand side is of the order of amplitude of the disturbance, and we therefore expect that (4.1) is a good approximation for small amplitude. Also explain its implication in the analysis of the equation