Pointwise decay and smoothness for semilinear elliptic equations and travelling waves

TL;DR

This paper establishes precise decay rates and smoothness properties of solutions to certain semilinear nonlocal elliptic equations, with applications to traveling wave solutions in fluid dynamics and plasma physics.

Contribution

It provides new sharp decay estimates and holomorphic extension results for solutions of a class of semilinear nonlocal elliptic equations, extending understanding of traveling waves in physical models.

Findings

Derived sharp decay estimates for solutions.

Proved holomorphic extensions of solutions.

Applied results to traveling waves in fluid and plasma physics.

Abstract

We derive sharp decay estimates and prove holomorphic extensions for the solutions of a class of semilinear nonlocal elliptic equations with linear part given by a sum of Fourier multipliers with finitely smooth symbols at the origin. Applications concern the decay and smoothness of travelling waves for nonlinear evolution equations in fluid dynamics and plasma physics.