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Information × Registration Number 0225U003248, (0123U104924) , R & D reports Title Evolution of solitary waves of different initial profiles in elastic materials. popup.stage_title Аналіз еволюції (побудова сценаріїв поширення) початкових профілів плоских хвиль Гаусса (симетричний профіль) та Уіттекера (несиметричний профіль). Числове моделювання. Head Rushchytskyi Yarema Ya., Доктор фізико-математичних наук Registration Date 06-06-2025 Organization S.P. Tymoshenka Institute of Mechanics of the National Academy of Sciences of Ukraine popup.description1 The purpose of the work is to study the evolution (construction of propagation scenarios) of solitary waves with initial profiles of various types that propagate in elastic nonlinear materials. popup.description2 The aim of the work is to develop a methodology for constructing mechanical models that describe the propagation of plane longitudinal waves, the initial profiles of which are described by a symmetric profile in the form of a Gaussian function, and an asymmetric profile in the form of a Whittaker function. The research methods are analytical and numerical. Within the framework of the Mernaghan model, a nonlinear plane longitudinal elastic displacement wave has been theoretically and numerically studied for two types of initial profiles, which correspond to the Gaussian (symmetric) and Uttucker (asymmetric) functions. The main novelty is that the evolution of waves is analyzed by an approximate method taking into account the first two and three approximations of the solution of the wave equation, the second approximation is used to compare with the third and identify new nonlinear effects. Some significant differences between the evolution of waves are shown. First, the symmetric and asymmetric initial profiles are transformed as a result of evolution in different ways. Second, the third approximation within the framework of the analysis by the method of constraints on the displacement gradient adds to the existing 1st and 2nd a third and thereby changes the symmetric wave profile to an asymmetric one in the case of a Gaussian wave. The third approximation allows us to observe new wave effects of the numerical analysis of the Gaussian and Whittaker waves. The initial Gaussian wave profile is deformed significantly and almost preserves the symmetry of the profile, which is accompanied by the decomposition of one hump into two humps, revealing two nonlinear wave effects - not the same slopes of the humps on the left and right and asymmetric displacements of the hump tops relative to the conventional vertical axis. The Whittaker wave profile (as an example of a wave with an asymmetric profile) deforms significantly and retains the asymmetric profile, which is accompa Product Description popup.authors Hamsheieva Olena A. Dashko Olha H. Romanova Nataliia V. Savelieva Kateryna V. Khotenko Iryna M. Khotenko Olena O. Yurchuk Vasyl M. popup.nrat_date 2025-06-06 Close