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D'Alembert type traveling wave solution for wave equations on a finite interval with coupled initial boundary conditions

In this paper, we study coupled wave equations which are defined on a semi‐infinite interval and a finite interval, respectively, and obtain their d'Alembert type traveling wave solutions with finite closed forms. We also illustrate the results by concrete examples. These results generalized the corresponding ones for single wave equation wherein the solution is usually expressed by Fourier series.