Using Bernoulli Equation to Solve Burger's Equation

Decay Mode Solutions to (2 + 1)-Dimensional Burgers Equation, Cylindrical Burgers Equation and Spherical Burgers Equation

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...

Heat Equation and Potential Burgers Equation

In this work, we construct the general solution to the Heat Equation (HE) and to many tensor structures associated to the Heat Equation, such as Symmetries, Lagrangians, Poisson Brackets (PB) and Lagrange Brackets (LB), using newly devised techniques that may be applied to any linear equation (e.g., Schrödinger Equation in field theory, or the small-oscillations problem in mechanics). In partic...

Convergence of iterative methods applied to Burgers-Huxley equation

Solving Burgers' Equation Using Optimal Rational Approximations

Abstra t. We solve vis ous Burger's equation using a fast and a urate algorithm referred to here as the redu tion algorithm for omputing near optimal rational approximations. Given a proper rational fun tion with n poles, the redu tion algorithm omputes (for a desired L ∞ -approximation error) a rational approximation of the same form, but with a (near) optimally small number m ≪ n of poles. Al...

Instantons in Burgers Equation

The instanton solution for the forced Burgers equation is found. This solution describes the exponential tail of the probability distribution function of velocity differences in the region where shock waves are absent. The results agree with the one found recently by Polyakov, who used the operator product conjecture. If this conjecture is true, then our WKB asymptotics of the Wyld functional i...