Exact solutions of the Swift-Hohenberg equation with dispersion
Nikolay A. Kudryashov, Dmitry I. Sinelshchikov
TL;DR
This paper derives exact traveling wave solutions for the Swift-Hohenberg equation with dispersion, classifies these solutions, and compares them to the non-dispersive case which admits only stationary solutions.
Contribution
It provides the first explicit classification of traveling wave solutions for the dispersive Swift-Hohenberg equation.
Findings
Traveling wave solutions are explicitly constructed.
Solutions are classified into different types.
Non-dispersive case admits only stationary solutions.
Abstract
The Swift-Hohenberg equation with dispersion is considered. Traveling wave solutions of the Swift-Hohenberg equation with dispersion are presented. The classification of these solutions is given. It is shown that the Swift-Hohenberg equation without dispersion has only stationary meromorphic solution.
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