Linear and nonlinear propagation of a pulsed sound beam in a dissipative fluid

1991 ◽  
Vol 89 (4B) ◽  
pp. 1929-1929
Author(s):  
Kjell‐Eivind Frøysa
Keyword(s):  
Nonlinear Propagation ◽  
Sound Beam ◽  
Linear And Nonlinear ◽  
Dissipative Fluid

scholarly journals Linear and nonlinear propagation of optical Nyquist pulses in fibers

2012 ◽  
Vol 20 (18) ◽  
pp. 19836 ◽  
Author(s):  
Toshihiko Hirooka ◽  
Masataka Nakazawa
Keyword(s):  
Nonlinear Propagation ◽  
Nyquist Pulses ◽  
Linear And Nonlinear

QUALITATIVE ANALYSIS OF THE KHOKHLOV–ZABOLOTSKAYA–KUZNETSOV (KZK) EQUATION

2008 ◽  
Vol 18 (05) ◽  
pp. 781-812 ◽  
Author(s):  
ANNA ROZANOVA-PIERRAT
Keyword(s):  
Blow Up ◽  
Viscous Medium ◽  
Finite Amplitude ◽  
Mean Value ◽  
Nonlinear Propagation ◽  
Step Method ◽  
Fractional Step Method ◽  
Sound Beam ◽  
Kzk Equation ◽  
Zero Viscosity

The Khokhlov–Zabolotskaya–Kuznetzov (KZK) equation is considered as a model of nonlinear acoustic which describes the nonlinear propagation of a finite-amplitude focused sound beam which is essentially one-directional, in the thermo-viscous medium.1,7,8 The aim of this paper is the study of the existence, uniqueness, stability, regularity, continuous dependence on the initial value and blow-up of solution of the KZK equation in Sobolev spaces Hs of periodic on x functions and with mean value zero. Existence of shock waves for the model with zero viscosity is proved using S. Alinhac's method.2 Global existence in time of the beam's propagation in viscous media is established for small enough initial data. Existence result is proved by two methods: first by the fractional step method in the particular case ℝ3 and s = 3 to justify the numerical results of Thierry Le Pollès25 and second for the general case ℝn and s > [n/2] + 1 by the approach used in Refs. 12 and 13 for the Kadomtsev–Petviashvili (KP) equation.

scholarly journals Numerical analysis of weak acoustic shocks in aperiodic array of rigid scatterers

2020 ◽  
Author(s):  
Michael Muhlestein ◽  
Carl Hart
Keyword(s):  
Numerical Experiments ◽  
Periodic Structures ◽  
Nonlinear Propagation ◽  
Nonlinear Frequency ◽  
Relative Importance ◽  
Frequency Content ◽  
Rectangular Waveguides ◽  
Initial Shock ◽  
Linear And Nonlinear ◽  
Kzk Equation

Nonlinear propagation of shock waves through periodic structures have the potential to exhibit interesting phenomena. Frequency content of the shock that lies within a bandgap of the periodic structure is strongly attenuated, but nonlinear frequency-frequency interactions pumps energy back into those bands. To investigate the relative importance of these propagation phenomena, numerical experiments using the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation are carried out. Two-dimensional propagation through a periodic array of rectangular waveguides is per-formed by iteratively using the output of one waveguide as the input for the next waveguide. Comparison of the evolution of the initial shock wave for both the linear and nonlinear cases is presented.

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