Инд. авторы:	Chirkunov Y.A.
Заглавие:	Invariant solutions of the Westervelt model of nonlinear hydroacoustics without dissipation
Библ. ссылка:	Chirkunov Y.A. Invariant solutions of the Westervelt model of nonlinear hydroacoustics without dissipation // International Journal of Non-Linear Mechanics. - 2016. - Vol.85. - P.41-53. - ISSN 0020-7462. - EISSN 1878-5638.
Внешние системы:	DOI: 10.1016/j.ijnonlinmec.2016.05.009; SCOPUS: 2-s2.0-84973322838;
Реферат:	eng: We study three-dimensional Westervelt model of a nonlinear hydroacoustics without dissipation. We received all of its invariant submodels. We studied all invariant submodels described by the invariant solutions of rank 0 and 1. All invariant solutions of rank 0 and 1 are found either explicitly, or their search is reduced to the solution of the nonlinear integral equations. With a help of these invariant solutions we researched: (1) a propagation of the intensive acoustic waves (self-similar, axisymmetric, planar and one-dimensional) for which the acoustic pressure and a speed of its change, or the acoustic pressure and its derivative in the direction of one of the axes are specified at the initial moment of the time at a fixed point, (2) a spherically symmetric ultrasonic field for which the acoustic pressure and a speed of its change, or the acoustic pressure and its radial derivative are specified at the initial moment of the time at a fixed point. Solving of the boundary value problems describing these processes is reduced to the solving of nonlinear integral equations. We are established the existence and uniqueness of solutions of these boundary value problems under some additional conditions. Mechanical relevance of the obtained solutions is as follows: (1) these solutions describe nonlinear and diffraction effects in ultrasonic fields of a special kind, (2) these solutions can be used as a test solutions in the numerical calculations performed in studies of ultrasonic fields generated by powerful emitters. We found all the conservation laws of the first order for the Westerveld equation written in dimensionless variables. © 2016 Elsevier Ltd.
Ключевые слова:	Submodels; Numerical calculation; Nonlinear integral equations; Invariant solutions; Existence and uniqueness of solution; Dimensionless variables; Diffraction effects; Underwater acoustics; Nonlinear equations; Concrete beams and girders; Boundary value problems; Acoustic waves; Acoustic wave propagation; Ultrasonic field; Nonlinear Westervelt model of hydroacoustics; Invariant submodels; Intensive acoustic waves; Integral equations; Ultrasonic field;
Издано:	2016
Физ. характеристика:	с.41-53