New Exact Solutions of Khokhlov–Zabolotskaya–Kuznetsov Equation
نویسنده
چکیده
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 considered.
منابع مشابه
On 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 کاملStable-Range Approach to Short Wave and Khokhlov-Zabolotskaya Equations
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 non...
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 کاملA new fractional sub-equation method for solving the space-time fractional differential equations in mathematical physics
In this paper, a new fractional sub-equation method is proposed for finding exact solutions of fractional partial differential equations (FPDEs) in the sense of modified Riemann-Liouville derivative. With the aid of symbolic computation, we choose the space-time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation in mathematical physics with a source to illustrate the validity a...
متن کامل