Stable-Range Approach to Short Wave and Khokhlov-Zabolotskaya Equations
نویسنده
چکیده
Short wave equations were introduced in connection with the nonlinear reflection of weak shock waves. They also relate to the modulation of a gas-fluid mixture. Khokhlov-Zabolotskaya equation are used to describe the propagation of a diffraction sound beam in a nonlinear medium. We give a new algebraic method of solving these equations by using certain finite-dimensional stable range of the nonlinear terms and obtain large families of new explicit exact solutions parameterized by several functions for them. These parameter functions enable one to find the solutions of some related practical models and boundary value problems.
منابع مشابه
New Exact Solutions of Khokhlov–Zabolotskaya–Kuznetsov Equation
Khokhlov–Zabolotskaya–Kuznetsov equation (φt + φφx − αφxx)x − 1/2(φyy + φzz) = 0 and its solutions are analyzed. A series of complete exact analytical solutions related to the one-dimensional and vectorial inhomogeneous Burgers equation are presented. A concrete example which corresponds to a special form of the inhomogeneous term is analyzed. Reduction to the traveling wave solution is conside...
متن کاملGroup Classification of a Nonlinear Sound Wave Model
Based on a recent classification of subalgebras of the symmetry algebra of the Zabolotskaya-Khokhlov equation, all similarity reductions of this equation into ordinary differential equations are obtained. Large classes of group invariant solutions of the equation are also determined, and some properties of these solutions are discussed.
متن کاملNonlinear acoustic wave equations with fractional loss operators.
Fractional derivatives are well suited to describe wave propagation in complex media. When introduced in classical wave equations, they allow a modeling of attenuation and dispersion that better describes sound propagation in biological tissues. Traditional constitutive equations from solid mechanics and heat conduction are modified using fractional derivatives. They are used to derive a nonlin...
متن کاملOn similarity solutions of Zabolotskaya-Khokhlov equation
The new closed form solutions of the (2+1)-dimensional Zabolotskaya–Khokhlov equation are constructed by using the similarity transformations method via Lie group theory. The Zabolotskaya–Khokhlov equation has been reduced into a new partial differential equation with smaller number of independent variables. Further using the similarity transformations method the new partial differential equati...
متن کاملA New Method of Ultrasonic Hydrophone Calibration using Wave Propagation Modeling
A new method is presented for hydrophone calibration using the Khokhlov Zabolotskaya Kuznetsov (KZK) equation. Simulated and experimental on-axis finite amplitude distortion time waveforms and frequency spectra are compared. The hydrophone calibration up to 100 MHz is estimated for two different hydrophones.
متن کامل