منابع مشابه
Noncommutative Burgers Equation
We present a noncommutative version of the Burgers equation which possesses the Lax representation and discuss the integrability in detail. We find a noncommutative version of the Cole-Hopf transformation and succeed in the linearization of it. The linearized equation is the (noncommutative) diffusion equation and exactly solved. We also discuss the properties of some exact solutions. The resul...
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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...
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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...
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We consider multidimensional stochastic Burgers equation on the torus T and the whole space R . In both cases we show that for positive viscosity ν > 0 there exists a unique strong global solution in L for p > d. In the case of torus we also establish a uniform in ν a priori estimate and consider a limit ν ↘ 0 for potential solutions. In the case of R uniform with respect to ν a priori estimate...
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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...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 2003
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/36/48/006