A special form of solution to half-wave equations

Hyungjin Huh

doi:10.3934/eect.2021056

Article Contents

2022, Volume 11, Issue 5: 1605-1612. Doi: 10.3934/eect.2021056

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A special form of solution to half-wave equations

Hyungjin Huh^,

Department of Mathematics, Chung-Ang University, Seoul 156-756, Republic of Korea

^* Corresponding author: Hyungjin Huh
^* Corresponding author: Hyungjin Huh

Received: April 2021

Revised: August 2021

Early access: October 2021

Published: October 2022

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government (MSIT) (2020R1F1A1A01072197)

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Abstract

We investigate a special form of solution to the one-dimensional half-wave equations with particular forms of nonlinearities. Using the special form of solution involving Hilbert transform, the half-wave equations reduce to nonlocal nonlinear transport equation which can be solved explicitly.

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Mathematics Subject Classification: Primary: 35L45; Secondary: 35F25.

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References

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