Instability of solitary waves of two-dimensional Benjamin equation

Esfahani A.
March 2023 Springer-Verlag Italia s.r.l.

Rendiconti del Circolo Matematico di Palermo
2023 #72 Issue 2 1437 - 1452 pp.

In this paper, we study instability of solitary wave solutions of the generalized two space-dimensional Benjamin equation (ut+uxxx-βHuxx+(up)x)x=uyy. This equation governs the evolution of waves at the interface of a two-fluid system in which surface-tension effects cannot be ignored. We improve the previous work by Chen et al. (Proc R Soc A 464:49–64, 2008, https://doi.org/10.1098/rspa.2007.0013) to the case β< 0 and p> 7 / 3 , and show that solitary waves of this equation are unstable by the mechanism of blow-up.

Blow-up , Solitary wave , Stability , Two dimensional Benjamin equation

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Department of Mathematics, Nazarbayev University, Nur-Sultan, 010000, Kazakhstan

Department of Mathematics

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