Exact meromorphic stationary solutions of the real cubic Swift-Hohenberg equation

TL;DR

This paper classifies all meromorphic stationary solutions of the real cubic Swift-Hohenberg equation, showing they are elliptic or degenerate elliptic, and explicitly constructs them, including a potentially new elliptic solution.

Contribution

It provides a complete classification and explicit construction of meromorphic solutions for the stationary real cubic Swift-Hohenberg equation, revealing a new elliptic solution.

Findings

All meromorphic solutions are elliptic or degenerate elliptic.

Explicit solutions are obtained via the subequation method.

Identification of a potentially new elliptic solution.

Abstract

We show that all meromorphic solutions of the stationary reduction of the real cubic Swift-Hohenberg equation are elliptic or degenerate elliptic. We then obtain them all explicitly by the subequation method, and one of them appears to be a new elliptic solution.