The symmetry for two class of steady stratified periodic water waves

TL;DR

This paper proves symmetry properties of two classes of steady stratified periodic water waves, using maximum principles and monotonicity assumptions, advancing understanding of wave structure under different physical conditions.

Contribution

It establishes symmetry results for stratified water waves with and without stagnation points, under various physical assumptions, using novel mathematical techniques.

Findings

Symmetry for waves without stagnation using maximum principle

Symmetry for waves with stagnation assuming monotonicity

Extension of symmetry results to different physical wave conditions

Abstract

In this paper, we mainly consider two class of travelling stratified periodic water waves, one with negative (or without) surface tension and the other with constant Bernoulli's function and stagnation points. We first establish the symmetry result for stratified water waves with negative (or without) surface tension, but without stagnation by using the modified maximum principle. Furthermore, the symmetry property of stratified water waves with constant Bernoulli's function and stagnation points is also obtained provided the monotonic property is known.