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			<titleStmt><title level='a'>Whitham modulation equationsfor the regularized Boussinesq equationwith cubic nonlinearity</title></titleStmt>
			<publicationStmt>
				<publisher>Cambridge University Press</publisher>
				<date>01/01/2026</date>
			</publicationStmt>
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				<bibl> 
					<idno type="par_id">10702328</idno>
					<idno type="doi">10.1017/jnw.2026.10042</idno>
					<title level='j'>Journal of Nonlinear Waves</title>
<idno>3033-4268</idno>
<biblScope unit="volume">2</biblScope>
<biblScope unit="issue"></biblScope>					

					<author>Mark A Hoefer</author><author>Anna Vainchtein</author>
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			<abstract><ab><![CDATA[A regularized Boussinesq equationis studied as a dispersive, long-wave (quasicontinuum) approximation of the Fermi–Pasta–Ulam lattice with a general cubic interaction force. Explicit periodic travelling wave solutions in terms of Jacobi elliptic functions are classified, and their solitary-wave, kink and trigonometric limits are obtained. The Whitham modulation equationsdescribing slow modulations of periodic travelling wave solutions are derived using an averaged variational principle. The convexity (strict hyperbolicity, genuine nonlinearity) of the resulting hydrodynamic-type equationsis examined numerically in general and analytically in the solitary-wave and harmonic limits. In particular, the loss of hyperbolicity and the formation of complex conjugate characteristic velocities is shown to lead to modulational instability of periodic travelling waves. The onset of modulational instability is verified by numerical computations of linearized spectra for periodic travelling waves and initial value problems that also reveal additional short-wavelength instabilities.]]></ab></abstract>
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