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A conditionally integrable non-reciprocal wave equation with diode properties

journal contribution
posted on 2025-04-09, 06:48 authored by Philip BroadbridgePhilip Broadbridge, JM Goard
A known class of conditionally integrable partial differential equations is extended to include those that can be reduced by a non-classical symmetry to a linear Kirchhoff equation. From any steady solution to that linear equation, there follows an exact time-dependent solution to a nonlinear hyperbolic equation. An example solution is constructed in two space dimensions and one time dimension. By a change of variable, in one space dimension these nonlinear partial differential equations are equivalent to a nonlinear wave equation with diode-like properties that break reciprocity. These properties are illustrated by an exact solution in one dimension.

Funding

This work was supported by the Australian Research Council [grant number DP220101680].

History

Publication Date

2025-06-01

Journal

Wave Motion

Volume

136

Article Number

103529

Pagination

9p.

Publisher

Elsevier

ISSN

0165-2125

Rights Statement

© 2025 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

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