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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.

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
Full Text: DOI
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