Ponomarev, D. (2022). A Note on the Appearance of the Simplest Antilinear ODE in Several Physical Contexts. AppliedMath, 2(3), 433–445. https://doi.org/10.3390/appliedmath2030024
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)=𝑓(𝑥)𝑢(𝑥) or its nonhomogeneous version 𝑢′(𝑥)=𝑓(𝑥)𝑢(𝑥)+𝑔(𝑥), 𝑥∈(0,𝑥0)⊂ℝ. We point out some of the advantages of the proposed reformulation and call for further investigation of the obtained ODE.
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Project title:
Analytische, numerische und: I 3538-N32 (FWF - Österr. Wissenschaftsfonds)
CC BY 4.0
