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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.

74J35 Solitary waves in solid mechanics
74E30 Composite and mixture properties
74H55 Stability of dynamical problems in solid mechanics
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