Steady motions of a continuous medium, resonances and Lagrangian turbulence

Exact Solutions of a Coupled Burgers System

“…The Burgers equation q t + q xx + 2qq x = 0 (1) is one of the most important nonlinear systems and a diversity of nonlinear phenomena can be explained by this simple model. [2] Recently some kinds of extensions of the model have been proposed. [3−5] In this paper, we study the following new extension of the Burgers equation: p t + p xx + 2pp x + 2cqq x = 0 , q t + q xx + 2(pq) x = 0 .…”

Symmetry study of the coupled Burgers system

“…Whence the recursion operator is found the infinitely many local symmetries can be obtained by repeated acting the operator on some simple known local symmetries such as the space-time translations and scaling transformations. About ten years ago, one of the present author (Lou) had pointed out that the infinitely many nonlocal symmetries can be simply constructed via acting the inverse recursion operator on the identity transformation [3] and the conformal transformations [4].The BuergerÕs equationis one of the most important nonlinear systems and a diversity of nonlinear phenomena can be explained by this simple model [5]. Recently many kinds of extensions of the model have been proposed [6][7][8].…”

“…is one of the most important nonlinear systems and a diversity of nonlinear phenomena can be explained by this simple model [5]. Recently many kinds of extensions of the model have been proposed [6][7][8].…”

“…The recursion operator of the ACBE can be easily obtained from that of the SCBE because of the well know transformation theorem [11] and the transformation relation (5). The result reads…”