On the solitons and nonlinear wave equations

The paper is focused on the solitons and nonlinear equations for an uniaxial deformation problem. The aim is to determine a parametrical representation for a class of constitutive laws for nonhomogeneous media for which the motion equations attached to a material system, is associated to a pseudospherical surface (with negative Gaussian curvature K). A subclass of these constitutive laws can be associated to a Tzitzeica surface, for which the ratio K/d4(d is the distance from the origin to the tangent plane at an arbitrary point), is constant. A genetic algorithm is performed to study three inverse problems associated to some experimental results.

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