Spectral representation of solution of cubically nonlinear equation for the Riemann simple wave

Гусев, В. А.; Makov, Yu. N.

doi:10.1134/s1063771010050040

Cited by 6 publications

(4 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(18). Substituting the complex field representa tions (9) in (13) leads to the interconnection between the complex amplitudes (20) As a result, expression (19) or (20), with allowance for (17), yields…”

Section: (13)mentioning

confidence: 97%

“…The total field of the particle velocity is obtained by the sum of (37) and (43), According to one of the findings in [18], if the medium is characterized by cubic nonlinearity, i.e., when both the second order physical nonlinearity and the geo metric nonlinearity of the second and third orders are absent, the amplitude of the third harmonic linearly increases with increasing distance on the initial part of the path. This agrees with (48) (see the first term).…”

Section: The Case Of the Boundary Condition For The Particle Velocitymentioning

confidence: 98%

“…In the one dimensional case, the wave equation for is obtained if we apply the D'Alembert operator to (18) taking into account (15) for on the right hand side,…”

Section: The Case Of the Boundary Condition For The Particle Velocitymentioning

confidence: 99%

See 2 more Smart Citations

Problems in using nonlinear collinear processes in third-order acoustical tomography

et al. 2012

View full text Add to dashboard Cite

The processes of acoustical generation of the third order wave harmonic by nonlinear collinear interaction of the pure third order and the twofold interaction of the second order are considered. It is shown that, in tomography schemes that are based on collinear interaction of waves, the interfering signal consider ably exceeds the useful signal that brings information on the acoustical nonlinear parameter of the third order already over short wave propagations. The solutions to the Burgers' equation and the Riemann waves equa tion have been numerically modeled to verify theoretical results. It is concluded that, using the nonlinear third order effects in diagnostics becomes possible only when the tomography schemes are based on the non collinear interaction of waves.Keywords: third order nonlinear tomography, nonlinear acoustical parameters of the second and third order, Burgers' equation, Riemann waves equation, nonlinear interrelations between the acoustical characteristics (particle velocity and phase velocity, pressure, density).

show abstract

Section: (13)mentioning

confidence: 97%

Section: The Case Of the Boundary Condition For The Particle Velocitymentioning

confidence: 98%

See 1 more Smart Citation

Problems in using nonlinear collinear processes in third-order acoustical tomography

et al. 2012

View full text Add to dashboard Cite

show abstract

“…[18]. In the expansion (19), which contains only odd harmonics, E n is the Weber function and J n is the Bessel function.…”

Section: Examples Of Physical Systems With Quadratically Cubic Nonlinmentioning

confidence: 99%

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

Руденко

Hedberg

2016

Nonlinear Dyn

View full text Add to dashboard Cite

compression can be stable, but shocks of rarefaction as well. The formation of stationary waves with finite width of shock front resulting from the competition between nonlinearity and dissipation is traced. Singlepulse propagation is studied by computer modeling. The nonlinear evolutions of N-and S-waves in a dissipative QC medium are described, and the transformation of a harmonic wave to a sawtooth-shaped wave with periodically recurring trapezoidal teeth is analyzed.

show abstract

Self-Similar Acoustic Waves in Homogeneous Media with Different-Modulus Nonlinearity and Relaxation

Назаров

Радостин

Kiyashko

2015

Radiophys Quantum El

View full text Add to dashboard Cite

Spectral representation of solution of cubically nonlinear equation for the Riemann simple wave

Cited by 6 publications

References 4 publications

Problems in using nonlinear collinear processes in third-order acoustical tomography

Problems in using nonlinear collinear processes in third-order acoustical tomography

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

Self-Similar Acoustic Waves in Homogeneous Media with Different-Modulus Nonlinearity and Relaxation

Contact Info

Product

Resources

About