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Instability of solitary waves in nonlinear composite media. (English. Russian original) Zbl 1036.74029
J. Appl. Math. Mech. 65, No. 6, 977-984 (2001); translation from Prikl. Mat. Mekh. 65, No. 6, 1008-1016 (2001).
The authors studies plane wave motions in inhomogeneous nonlinear elastic medium (composite). It is assumed that the displacements $$w_\alpha$$, the strains $$u_\alpha = \partial w_\alpha/\partial x$$ and the velocities of particles $$v_\alpha$$ $$(\alpha = 1,2,3)$$ depend on a single Cartesian coordinate $$x_3$$ and on time $$t$$. Basic equations describing plane waves are presented, their Hamiltonian form is found, and symmetries in anisotropic and isotropic cases are studied. The authors also discuss the instability of solitary waves.

##### MSC:
 74J35 Solitary waves in solid mechanics 74E30 Composite and mixture properties 74H55 Stability of dynamical problems in solid mechanics
##### Keywords:
plane wave; anisotropy; isotropy; Hamiltonian equations; symmetries
##### References:
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