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تسجيل مستخدم جديدLinearizability of the Perturbed Burgers Equation
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We show in this letter that the perturbed Burgers equation $u_t = 2uu_x + u_{xx} + epsilon ( 3 alpha_1 u^2 u_x + 3alpha_2 uu_{xx} + 3alpha_3 u_x^2 + alpha_4 u_{xxx} )$ is equivalent, through a near-identity transformation and up to order epsilon, to a linearizable equation if the condition $3alpha_1 - 3alpha_3 - 3/2 alpha_2 + 3/2 alpha_4 = 0$ is satisfied. In the case this condition is not fulfilled, a normal form for the equation under consideration is given. Then, to illustrate our results, we make a linearizability analysis of the equations governing the dynamics of a one-dimensional gas.
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