Forced Nonlinear Waves Governed by Inhomogeneus Burgers Equation

E.A.Lapshin (Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia)


Excitation and propagation nonlinear processes governed by inhomogeneous Burgers equation with non-zero right-hand-side (r-h-s) are considered. By use of characteristics method both qualitative and quantitative properties of solutions for arbitrary forms of r-h-s are studied. The temporal profiles are calculated, all the principal parameters are determined: the coordinate of shock front formation, the velocity of propagation, the peak magnitudes of the disturbance. It was shown, that at large distances the solution reaches its stationary form depending on the properties of r-h-s. Unusual properties demonstrates the steady-state solution for the random r-h-s. It is shown, that fluctuations of "drioving force" in the r-h-s of inhomogeneous Burgers equation excite the acoustic noise wave at small distances, but the corresponding steady-state solution is much more "smoothed". Concequently, we observe the nonlinear "chaos-order" transformation.


Section : 1