Approximate symmetry reduction approach: infinite series reductions to the KdV-Burgers equation

Details Approximate symmetry reduction approach: infinite series reductions to the KdV-Burgers equation Approximate symmetry reduction approach: infinite series reductions to the KdV-Burgers equation

2008-01-06

arxiv.org/abs/0801.0856v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

14 pages. The original model (1) in previous version is generalized to a more extensive form and the incorrect equations (35)

Scientific paper

For weak dispersion and weak dissipation cases, the (1+1)-dimensional KdV-Burgers equation is investigated in terms of approximate symmetry reduction approach. The formal coherence of similarity reduction solutions and similarity reduction equations of different orders enables series reduction solutions. For weak dissipation case, zero-order similarity solutions satisfy the Painlev\'e II, Painlev\'e I and Jacobi elliptic function equations. For weak dispersion case, zero-order similarity solutions are in the form of Kummer, Airy and hyperbolic tangent functions. Higher order similarity solutions can be obtained by solving linear ordinary differential equations.

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