Absence of traveling wave solutions of conductivity type for the Novikov-Veselov equations at zero energy
Anna Kazeykina (CMAP)
TL;DR
This paper proves that the Novikov-Veselov equation at zero energy does not admit localized soliton solutions of conductivity type, highlighting a fundamental limitation in its solution structure.
Contribution
It establishes the non-existence of certain localized soliton solutions for the Novikov-Veselov equation at zero energy, a significant theoretical result.
Findings
No localized soliton solutions of conductivity type exist at zero energy
The result extends understanding of solution limitations for the Novikov-Veselov equation
Provides insights into the behavior of analogs of KdV in higher dimensions
Abstract
We prove that the Novikov-Veselov equation (an analog of KdV in dimension 2 + 1) at zero energy does not have sufficiently localized soliton solutions of conductivity type.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Waves and Solitons · Nonlinear Photonic Systems