Solutions for Nonlinear Plane‐Wave Equations of Acoustics by the Method of Functional Interrelationships of Dependent Variables

1964 ◽  
Vol 36 (5) ◽  
pp. 1031-1032
Author(s):  
Verner J. Raelson
Keyword(s):  
Plane Wave ◽  
Wave Equations ◽  
Dependent Variables ◽  
Nonlinear Plane

Plane-wave propagation in media with electromagnetic anisotropy

2021 ◽  
Author(s):  
David Romero-Abad ◽  
Jose Pedro Reyes Portales ◽  
Roberto Suárez-Córdova
Keyword(s):  
Plane Wave ◽  
Electromagnetic Waves ◽  
Wave Equations ◽  
Refraction Index ◽  
Pedagogical Approach ◽  
Undergraduate Level ◽  
Quartic Equation ◽  
Principal Axes ◽  
The Subject ◽  
Magnetic Tensors

Abstract The propagation of electromagnetic waves in a medium with electrical and magnetic anisotropy is a subject that is not usually handled in conventional optics and electromagnetism books. During this work, we try to give a pedagogical approach to the subject, using tools that are accessible to an average physics student. In this article, we obtain the Fresnel relation in a media with electromagnetic anisotropy, which corresponds to a quartic equation in the refraction index, assuming only that the principal axes of the electric and magnetic tensors coincide. Additionally, we find the geometric location related to the different situations the discriminant of the quartic equation provides. In order to illustrate our findings, we determine the refractive index together with the plane wave equations for certain values of the parameters that meet the established conditions. The target readers of the paper are students pursuing physics at the intermediate undergraduate level.

scholarly journals Exact Solutions Superimposed with Nonlinear Plane Waves

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
B. S. Desale ◽  
Vivek Sharma
Keyword(s):  
Exact Solution ◽  
Plane Wave ◽  
Incompressible Fluid ◽  
Exact Solutions ◽  
Large Scale ◽  
Plane Waves ◽  
Boussinesq Equations ◽  
Integral Curves ◽  
Nonlinear Plane ◽  
Scale Motion

The flow of fluid in atmosphere and ocean is governed by rotating stratified Boussinesq equations. Through the literature, we found that many researchers are trying to find the solutions of rotating stratified Boussinesq equations. In this paper, we have obtained special exact solutions and nonlinear plane waves. Finally, we provide exact solutions to rotating stratified Boussinesq equations with large scale motion superimposed with the nonlinear plane waves. In support of our investigations, we provided two examples: one described the special exact solution and in second example, we have determined the special exact solution superimposed with nonlinear plane wave. Also, we depicted some integral curves that represent the flow of an incompressible fluid particle on the planex1+x2=L(constant)as the particular case.

MODULATIONAL INSTABILITY IN NONLINEAR BI-INDUCTANCE TRANSMISSION LINE

2005 ◽  
Vol 19 (26) ◽  
pp. 3961-3983 ◽  
Author(s):  
E. KENGNE ◽  
KUM K. CLETUS
Keyword(s):  
Plane Wave ◽  
Transmission Line ◽  
Traveling Waves ◽  
Modulational Instability ◽  
Ginzburg Landau ◽  
Complex Demodulation ◽  
Wave Solutions ◽  
Ginzburg Landau Equations ◽  
Nonlinear Plane ◽  
The Right

A nonlinear dissipative transmission line is considered and by performing the complex demodulation technique of the signal which allows, in particularly, to separate the right traveling and left traveling waves, we show that the amplitudes of these waves can be described by a complex coupled Ginzburg–Landau equations (CG-LE). The so-called phase winding solutions of the constructed CG-LE is analyzed. We also study the coherent structures in the obtained complex Ginzburg–Landau system. We show that the constructed CG-LE possesses nonlinear plane wave solutions and the modulational instability of these solutions is analyzed. The condition of the modulational instability is given in term of the coefficients of the constructed CG-LE and then in term of the wavenumber of the two right traveling and left traveling waves in the considered transmission line. The results obtained here show that the nonlinear plane wave solutions of the CG-LE under perturbation with zero wavenumber cannot be stable under modulation.

The Wavefield Radiated Into an Elastic Half-Space by a Transducer of Large Aperture

1988 ◽  
Vol 55 (2) ◽  
pp. 398-404 ◽  
Author(s):  
John G. Harris
Keyword(s):  
Power Series ◽  
Plane Wave ◽  
Half Space ◽  
Wave Equations ◽  
Ultrasonic Transducer ◽  
Elastic Half Space ◽  
The Other ◽  
Circular Region ◽  
Asymptotic Power ◽  
Normal Traction

The wavefield radiated into an elastic half-space by an ultrasonic transducer, as well as the radiation admittance of the transducer coupled to the half-space, are studied. Two models for the transducer are used. In one an axisymmetric, Gaussian distribution of normal traction is imposed upon the surface, while in the other a uniform distribution of normal traction is imposed upon a circular region of the surface, leaving the remainder free of traction. To calculate the wavefield, each wave emitted by the transducer is expressed as a plane wave multiplied by an asymptotic power series in inverse powers of the aperture’s (scaled) radius. This reduces the wave equations satisfied by the compressional and shear potentials to their parabolic approximations. The approximations to the radiated waves are accurate at a depth where the wavefield remains well collimated.

A NONLINEAR PLANE-WAVE ALGORITHM FOR DIFFRACTIVE PROPAGATION INVOLVING SHOCKWAVES

1993 ◽  
Vol 01 (03) ◽  
pp. 371-393 ◽  
Author(s):  
P. TED CHRISTOPHER
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Frequency Domain ◽  
Time Domain ◽  
Burgers Equation ◽  
Propagation Model ◽  
Nonlinear Beam ◽  
Nonlinear Plane ◽  
Very High ◽  
Plane Wave Propagation

A new algorithm for nonlinear plane-wave propagation is presented. The algorithm uses a novel time domain representation to account for nonlinearity, while accounting for absorption in the frequency domain. The new algorithm allows for accurate representations of diffractive shockwave propagation in the framework of an existing nonlinear beam propagation model using far fewer harmonics (and thus time) than alternative algorithms based on a frequency domain solution to Burgers' equation. The new algorithm is tested against the frequency domain solution to Burgers' equation in a variety of cases and then used to model a focused ultrasonic piston transducer operating at very high source intensities.

scholarly journals Stability and Instability of Traveling Wave Solutions to Nonlinear Wave Equations

2021 ◽  
Author(s):  
John Anderson ◽  
Samuel Zbarsky
Keyword(s):  
Plane Wave ◽  
Wave Equations ◽  
Traveling Wave Solutions ◽  
Linear Instability ◽  
Nonlinear Wave Equations ◽  
Null Condition ◽  
Semilinear Systems ◽  
Wave Solutions ◽  
Stability And Instability ◽  
The Stability

Abstract In this paper, we study the stability and instability of plane wave solutions to semilinear systems of wave equations satisfying the null condition. We identify a condition that allows us to prove the global nonlinear asymptotic stability of the plane wave. The proof of global stability requires us to analyze the geometry of the interaction between the background plane wave and the perturbation. When this condition is not met, we are able to prove linear instability assuming an additional genericity condition. The linear instability is shown using a geometric optics ansatz.

The effects of a corner on a propagating internal gravity wave

1970 ◽  
Vol 42 (2) ◽  
pp. 257-267 ◽  
Author(s):  
R. M. Robinson
Keyword(s):  
Plane Wave ◽  
Internal Wave ◽  
Wave Equations ◽  
Internal Gravity Wave ◽  
Radiation Condition ◽  
Ray Theory ◽  
Present Solution ◽  
Linear Internal Wave ◽  
Radiation Conditions ◽  
Infinite Wall

A solution satisfying the usual radiation conditions is found to the problem of an internal wave propagating towards a corner. It is found that, far from the corner, and the characteristic emanating from the corner, the solution is asymptotically equivalent to the solution found by plane wave reflexions from an infinite wall. The present solution shows that, by imposing the radiation condition, a singularity predicted by the ray theory along the corner characteristic is absent. A further singularity in the present solution along the same characteristic is shown to be due to an inability of the usual linear internal wave equations to fully describe the motion. The solution is for restricted corner angles.

NONLINEAR PLANE WAVES IN A LONG-WAVELENGTH CONVECTION MODEL

2001 ◽  
Vol 11 (11) ◽  
pp. 2867-2874
Author(s):  
A. M. MANCHO ◽  
L. VÁZQUEZ ◽  
H. HERRERO ◽  
S. HOYAS
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Plane Wave ◽  
Prandtl Number ◽  
Plane Waves ◽  
Long Wavelength ◽  
Wave Solutions ◽  
Convection Model ◽  
Nonlinear Plane

The partial differential equation (PDE) associated with the long-wavelength regime that describes convection between rigid and poorly conducting boundaries in an infinite Prandtl number fluid is studied in this document. This PDE is reduced to a set of ordinary differential equations (ODE) by looking for the exact nonlinear plane wave solutions. Solving this ODE several kinds of oscillatory attractors are obtained. These attractors are compared to oscillations observed in experiments on fluids and some features are also recovered.

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