{"title":"A conditionally integrable non-reciprocal wave equation with diode properties","authors":"P. Broadbridge , J.M. Goard","doi":"10.1016/j.wavemoti.2025.103529","DOIUrl":null,"url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"136 ","pages":"Article 103529"},"PeriodicalIF":2.1000,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Wave Motion","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S016521252500040X","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ACOUSTICS","Score":null,"Total":0}
引用次数: 0
Abstract
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.
期刊介绍：
Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics.
The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.
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