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<p>The question of the spectral stability of periodic waves of cnoidal and snoidal types for the Boussinesq equation is considered. The main results are that, for some values of the parameters, the periodic cnoidal waves are spectrally stable and unstable for others, with respect to perturbations of the same period. For the snoidal waves, we have that they are stable for all values of the parameters. Our approach, which turns out to give a definite answer for the entire domain of parameters, relies on the instability index theory, as developed by Lin and Zeng (Mem Am Math Soc 275(1347):136, 2022).</p>

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On the stability of the periodic traveling waves of the quadratic-cubic Boussinesq equation

  • 期刊论文

  • 发表日期：

    2026年5月6日

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  • Sevdzhan Hakkaev

摘要

The question of the spectral stability of periodic waves of cnoidal and snoidal types for the Boussinesq equation is considered. The main results are that, for some values of the parameters, the periodic cnoidal waves are spectrally stable and unstable for others, with respect to perturbations of the same period. For the snoidal waves, we have that they are stable for all values of the parameters. Our approach, which turns out to give a definite answer for the entire domain of parameters, relies on the instability index theory, as developed by Lin and Zeng (Mem Am Math Soc 275(1347):136, 2022).