The method of distributions is developed for systems that are governed by hyperbolic conservation laws with stochastic forcing. yields a deterministic equation the cumulative distribution function (CDF) system state, e.g., flow velocity an inviscid Burgers random source coefficients. This achieved without recourse to any closure approximation. CDF model verified against Monte Carlo (MC) simulat...

We detect so far unknown complex singularities in the temporal domain of inviscid Burgers equation one space dimension. The (early!) loss time-analyticity velocity is accompanied by appearance initially localized resonant behavior which, as we claim, a manifestation so-called tyger phenomenon, reported Galerkin-truncated implementations fluids. test two methods that reduce amplitude these tyger...

A nondispersive, conservative regularisation of the inviscid Burgers equation is proposed and studied. Inspired by a related shallow water system recently introduced Clamond Dutykh, new provides family Galilean-invariant interpolants between Hunter–Saxton equation. It admits weakly singular regularised shocks cusped traveling-wave weak solutions. The breakdown local smooth solutions demonstrate...

A meromorphic solution to the Burgers equation with complex viscosity is analysed. The equation is linearized via the Cole–Hopf transform which allows for a careful study of the behaviour of the singularities of the solution. The asymptotic behaviour of the solution as the dispersion coefficient tends to zero is derived. For small dispersion, the time evolution of the poles is found by numerica...

This work is devoted to investigating stochastic turbulence for the fluid flow in one-dimensional viscous Burgers equation perturbed by Lévy space-time white noise with periodic boundary condition. We rigorously discuss regularity of solutions and their statistical quantities this dynamical system. The include moment estimate, structure function energy spectrum turbulent velocity field. Further...

Three (2 + 1)-dimensional equations—Burgers equation, cylindrical Burgers equation and spherical Burgers equation, have been reduced to the classical Burgers equation by different transformation of variables respectively. The decay mode solutions of the Burgers equation have been obtained by using the extended G G ′       -expansion method, substituting the solutions obtained into the cor...

The Burgers’ equation first appeared in the paper by Bateman [3], who mentioned two of the essentially steady solutions. Due to extensive works of Burgers [4] involving the Burgers’ equation especially as a mathematical model for the turbulence, it is known as Burgers’ equation. The equation is used as a model in fields as wide as heat conduction [5], gas dynamics [13], shock waves [4], longitu...