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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.
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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