Integrability of the higher-order nonlinear Schroedinger equation revisited
S. Yu. Sakovich
TL;DR
This paper reviews the integrability of the higher-order nonlinear Schrödinger equation, confirming that only known cases pass the Painleve test and that recent findings do not introduce new integrable cases.
Contribution
It clarifies the integrability status of the equation by analyzing recent claims and reaffirming existing known integrable cases.
Findings
Only known integrable cases pass the Painleve test
Recent results do not identify new integrable cases
The integrability of the equation remains limited to established cases
Abstract
Only the known integrable cases of the Kodama-Hasegawa higher-order nonlinear Schroedinger equation pass the Painleve test. Recent results of Ghosh and Nandy add no new integrable cases of this equation.
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Taxonomy
TopicsNonlinear Waves and Solitons · Numerical methods for differential equations · Nonlinear Photonic Systems