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Perturbation around exact solutions for nonlinear dynamical systems: Application to the perturbed Burgers equation. (English) Zbl 0737.35100

Summary: When two dynamical systems of nonlinear partial differential equations differ by a term that can be considered as a perturbation, their solutions equal at the initial time , can be related by a linear integral equation. Due to this equation, if the solution of one of these systems is known, let us call it free, the solution of the other one, the perturbed one, can be written as a perturbation expansion, the terms of which are completely explicit expressions of the free solution. This generalizes the usual perturbation theories around free solutions satisfying linear equations. The perturbed Burgers equation is taken as an example.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35B20 Perturbations in context of PDEs
35K55 Nonlinear parabolic equations
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References:

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