We describe the dynamics of the Kirchhoff ellipse by formulating a nonlinear equation for the boundary of a perturbed vortex patch in elliptical coordinates. We demonstrate that in the regime for which the linearized equation of motion is unstable, the nonlinear dynamics of a rather general initial perturbation of the Kirchhoff ellipse are determined by the fastest growing mode for the correspo...

The acoustic backscatter from pressure release prolate spheroids and a three-dimensional representation of a fish swimbladder (Chilean jack mackerel, Trachurus symmetricus murphyi) was calculated using four target strength models (Kirchhoff-approximation, Kirchhoff-ray-mode, finite element solution of the Helmholtz equation, and prolate-spheroid-modal-series). Smoothly varying errors were found...

A generalized Kowalevski Hamiltonian and new integrable cases on e(3) and so(4). 1 A new integrable case for the Kirchhoff equation. The Kirchhoff equations (see for example [1]) for the motion of a rigid body in an ideal fluid read as follows M t = M × ∂H ∂M + Γ × ∂H ∂Γ , Γ t = Γ × ∂H ∂M ,

In this paper, we studied the long-time properties of solutions generalized Kirchhoff-type equation with strongly damped terms. Firstly, appropriate assumptions are made for nonlinear source term g (u) and Kirchhoff stress term M (s) in equation, existence uniqueness solution proved by using uniform prior estimates time Galerkin’s finite element method. Then, abounded absorption set B0k is obta...

In this paper, we study the asymptotic behavior of solutions to Kirchhoff type stochastic plate equation driven by additive noise defined on unbounded domains. We first prove uniform estimates and then establish existence upper semicontinuity random attractors.

We collect recent ideas on transforming integral operators for imaging/inversion that use quotients of wave fields into operators that use products of wave fields; that is, transforming deconvolution-type operators into correlation-type operators. The transformation avoids evaluation of extremely large or extremely small numbers; hence, the designation “computer-friendly.” For this author, “inv...