Linearizability of the Perturbed Burgers Equation

Abstract

We show in this letter that the perturbed Burgers equation $u_t=2u{u}_x+u_{xx}+\epsilon (3{\alpha }_1{u}^2{u}_x+3{\alpha }_{2}u{u}_{xx}+3{\alpha }_3{u}_x^2+{\alpha }_4{u}_{xxx})$ is equivalent, through a near-identity transformation and up to order ε, to a linearizable equation if the condition $3{\alpha }_1-3{\alpha }_3-3/2{\alpha }_2+3/2{\alpha }_4=0$ 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.

arXiv comment10 pages, RevTeX, no figures

References in corpus (1)

• Multiple-Time Higher-Order Perturbation Analysis of the Regularized Long-Wavelength Equation

Cited by in corpus (4)

• Extended models of nonlinear waves in liquid with gas bubbles
• Extended two dimensional equation for the description of nonlinear waves in gas-liquid mixture
• Analytical and numerical studying of the perturbed Korteweg--de Vries equation
• Perturbative analysis of wave interactions in nonlinear systems