Archives

  • Home/
  • Tag: oleg rudenko

Exact solutions of an integro-differential equation with quadratically cubic nonlinearity

ABSTRACT Exact solutions of a nonlinear integro-differential equation with quadratically cubic nonlinear term are found. The equation governs, in particular, stationary shock wave propagation in relaxing media. For the exponential kernel the shapes of both compression and rarefaction shocks having a finite width of the front are calculated. For media with limited “memorizing time” the […]

Sharing
       
Read More

Inverse problem of nonlinear acoustics: Synthesizing intense signals to intensify the thermal and radiation action of ultrasound

ABSTRACT Inverse problems of nonlinear acoustics have important applied significance. On the one hand, they are necessary for nonlinear diagnostics of media, materials, manufactured articles, building units, and biological and geological structures. On the other hand, they are needed for creating devices that ensure optimal action of acoustic radiation on a target. However, despite the […]

Sharing
       
Read More

Acoustic microfluidics: Capillary waves and vortex currents in a spherical fluid drop

ABSTRACT Self-similar solutions are found for a quadratically cubic second-order partial differential equation governing the behavior of nonlinear waves in various distributed systems, for example, in some metamaterials. They are compared with self-similar solutions of the Burgers equation. One of them describing a single unipolar pulse is shown to satisfy both equations. The other self-similar […]

Sharing
       
Read More

Self-similar solutions of a Burgers-type equation with quadratically cubic nonlinearity

ABSTRACT Self-similar solutions are found for a quadratically cubic second-order partial differential equation governing the behavior of nonlinear waves in various distributed systems, for example, in some metamaterials. They are compared with self-similar solutions of the Burgers equation. One of them describing a single unipolar pulse is shown to satisfy both equations. The other self-similar […]

Sharing
       
Read More

The quadratically cubic Burgers equation: an exactly solvable nonlinear model for shocks, pulses and periodic waves

ABSTRACT A modified equation of Burgers type with a quadratically cubic (QC) nonlinear term was recently pointed out as a new exactly solvable model of mathematical physics. However, its derivation, analytical solution, computer modeling, as well as its physical applications and analysis of corresponding nonlinear wave phenomena have not been published up to now. The […]

Sharing
       
Read More

A nonlinear screen as an element for sound absorption and frequency conversion systems

ABSTRACT The paper discusses a model for a screen with dissipative and nonlinear elastic properties that can be used in acoustic sound absorption and frequency conversion systems. Calculation and estimation schemes are explained that are necessary for understanding the functional capabilities of the device. Examples of the nonlinear elements in the screen and promising applications […]

Sharing
       
Read More