@article{Savelieva_Dashko_2022, title={Plane elastic wave interaction. Considering of quadratically and cubically nonlinearity}, url={https://bphm.knu.ua/index.php/bphm/article/view/320}, DOI={10.17721/1812-5409.2022/1.6}, abstractNote={<p><em>The interaction of elastic plane harmonic waves in the material, the nonlinear properties of which are </em><em>described by the elastic potential of Murnaghan, is investigated theoretically. The displacement vector is </em><em>depended of only one spatial variable and time, a record of the complete system of equations for plane waves </em><em>moves along the abscissa axis is recorded and used. The interaction of longitudinal waves with a separate </em><em>considering cubic nonlinearity is investigated. On the basis of the cubic equation of motion, the interaction </em><em>of four harmonic waves is studied. The method of slowly variable amplitudes is used. Firstly the two-wave </em><em>interaction is investigated, then the interaction of four waves is described. Shorten and evolutionary </em><em>equations are obtained, the first integrals of these equations and the record of the law of conservation for a </em><em>set of four interacting waves are obtained. An analogy is made between the triplets studied when taking into </em><em>account the interaction of three waves and the triplets investigated in the case under consideration, taking </em><em>into account the four-wave interaction, quadruplets.</em></p> <p><em><strong>Pages of the article in the issue</strong></em>: 50 - 53</p> <p><strong><em>Language of the article</em></strong>: Ukrainian</p>}, number={1}, journal={Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences}, author={Savelieva, K. V. and Dashko, O. G.}, year={2022}, month={Apr.}, pages={50–53} }