A Note on the Appearance of the Simplest Antilinear ODE in Several Physical Contexts

Abstract

We review several one-dimensional problems such as those involving linear Schrödinger equation, variable-coefficient Helmholtz equation, Zakharov–Shabat system and Kubelka–Munk equations. We show that they all can be reduced to solving one simple antilinear ordinary differential equation u′x=fxux¯ or its nonhomogeneous version u′x=fxux¯+gx, x∈0,x0⊂R. We point out some of the advantages of the proposed reformulation and call for further investigation of the obtained ODE.