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Lie group analysis and conservation laws for the time-fractional third order KdV-type equation with a small perturbation parameter. (English) Zbl 1448.76118
Summary: The KdV equation is one of the most famous PDEs which has a vast field of applications in fluid dynamics. The scope of our research is the Lie group analysis of time-fractional KdV-type equation including a perturbation term. Thus, the Lie group theory is extended to both cases simultaneously. Geometric vector fields of symmetries and one-dimensional optimal system are found in order to reduce the equation. Finally, approximated conservation laws are given via modified Ibragimov’s theorem.
MSC:
 76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics 76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction 76M45 Asymptotic methods, singular perturbations applied to problems in fluid mechanics 35Q53 KdV equations (Korteweg-de Vries equations)
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