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Instability of solitary waves for generalized Boussinesq equations. (English) Zbl 0784.34048
A nonlinear equation of Boussinesq type is considered. It is investigated the stability of the solitary wave solutions proving that a traveling wave may be stable or unstable, depending on the range of the wave’s speed of propagation and on the nonlinearity.

MSC:
34G20 Nonlinear differential equations in abstract spaces
35Q35 PDEs in connection with fluid mechanics
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
35L75 Higher-order nonlinear hyperbolic equations
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