On some classess of linearizable reaction-convection-diffusion equations
In this paper, we consider the class of equations ut = [F(x,u)ux + G(x, u)]x + H(x, u). Using hodograph and dependent variable transformations, we determine sufficient conditions on F, G, and H such that this equation is linearizable. We also derive a general quasilinear equation, which includes the Clarkson-Fokas-Ablowitz equation (SIAM J. Appl. Math. 49 (1989), 1188-1209), that can be transformed into semilinear form.