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arXiv · 2606.27185

Instability of periodic waves in generalized Korteweg-de Vries-Burgers equation with monostable source

Aarushi Kansal·Ashish Kumar Pandey
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Abstract

We study periodic traveling waves in a general class of nonlinear dispersive equations with Burgers dissipation and a monostable Fisher-KPP reaction source. Under natural assumptions on the dispersion symbol, we prove the existence of small-amplitude periodic traveling waves bifurcating from a constant equilibrium by means of a Lyapunov-Schmidt reduction. We then investigate the spectral stability of these waves by combining Floquet-Bloch decomposition with perturbation theory for linear operators. It is shown that the Floquet spectrum of the linearized operator intersects the unstable complex half-plane, implying spectral instability with respect to localized perturbations. The results recover the recently established instability theory for the Korteweg-de Vries-Burgers-Fisher equation as a special case and provide a unified framework for a broad class of local and nonlocal dispersive systems. These results reveal a common instability mechanism generated by the interplay of dispersion, Burgers dissipation, and monostable reaction dynamics.

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Aarushi Kansal, Ashish Kumar Pandey. 2026-06-25. Instability of periodic waves in generalized Korteweg-de Vries-Burgers equation with monostable source. https://arxiv.org/abs/2606.27185

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