$C^1$-smoothness of Nemytskii operators on Sobolev-type spaces of periodic functions

TL;DR

This paper proves the $C^1$-smoothness of Nemytskii operators on Sobolev spaces of periodic functions, which is crucial for analyzing nonlinear models in various scientific fields.

Contribution

It establishes the $C^1$-continuity of a broad class of Nemytskii operators on Sobolev-type spaces of periodic functions, covering models in laser, population, and chemical dynamics.

Findings

Proves $C^1$-smoothness of Nemytskii operators

Applies to models in laser, population, and chemical kinetics

Provides mathematical foundation for nonlinear analysis

Abstract

We consider a class of Nemytskii superposition operators that covers the nonlinear part of traveling wave models from laser dynamics, population dynamics, and chemical kinetics. Our main result is the $C^1$-continuity property of these operators over Sobolev-type spaces of periodic functions.