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<p style='text-indent:20px;'>We present an exact solution to the nonlinear governing equations in the <inline-formula><tex-math id="M1">\begin{document}$ \beta $\end{document}</tex-math></inline-formula>-plane approximation for geophysical edge waves at an arbitrary latitude. Such an exact solution is derived in the Lagrange framework, which describes trapped waves propagating eastward or westward along a sloping beach with a shoreline parallel to the latitude line. Using the short-wavelength instability method, we establish a criterion for the instability of such waves.</p>

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