Invariant and Partially Invariant Solutions of the Green-Naghdi Equations

Bagderina, Yu. Yu.; Чупахин, А. П.

doi:10.1007/s10808-005-0136-z

Cited by 11 publications

(5 citation statements)

References 5 publications

(6 reference statements)

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“…Since the automorphism A 4 for W ¼ Àaq À3 _ q 2 differs from the automorphism A 4 for the Green-Naghdi model, the subalgebras Y 1 þ cY 3 ; ðc-0Þ considered in [13] are here equivalent to Y 1 þ Y 3 .…”

Section: Remarkmentioning

confidence: 99%

Invariant solutions of the special model of fluids with internal inertia

Hematulin

Siriwat

2009

Communications in Nonlinear Science and Numerical Simulation

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Section: Remarkmentioning

confidence: 99%

Invariant solutions of the special model of fluids with internal inertia

Hematulin

Siriwat

2009

Communications in Nonlinear Science and Numerical Simulation

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“…The Green-Naghdi model belongs to the class M 7 in Table 1 with λ = 1, p = 2 and µ = 0. Invariant solutions of the one-dimensional Green-Naghdi model completely studied in [21].…”

Section: Case Dim(span(v )) =mentioning

confidence: 99%

Applications of Group Analysis to the Three-Dimensional Equations of Fluids with Internal Inertia

Siriwat¹,

Meleshko

2008

SIGMA

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Abstract. Group classification of the three-dimensional equations describing flows of fluids with internal inertia, where the potential function W = W (ρ,ρ), is presented. The given equations include such models as the non-linear one-velocity model of a bubbly fluid with incompressible liquid phase at small volume concentration of gas bubbles, and the dispersive shallow water model. These models are obtained for special types of the function W (ρ,ρ). Group classification separates out the function W (ρ,ρ) at 15 different cases. Another part of the manuscript is devoted to one class of partially invariant solutions. This solution is constructed on the base of all rotations. In the gas dynamics such class of solutions is called the Ovsyannikov vortex. Group classification of the system of equations for invariant functions is obtained. Complete analysis of invariant solutions for the special type of a potential function is given.

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“…Optimal system of subalgebras and invariant solutions for the Green-Naghdi model are completely studied in [14].…”

Section: Remarkmentioning

confidence: 99%

Group classification of one‐dimensional equations of fluids with internal inertia

Hematulin¹,

Meleshko²,

Gavrilyuk³

2007

Math Methods in App Sciences

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SUMMARYOne-dimensional flows of fluids with internal inertia are studied in the manuscript. The given equations include such models as the non-linear one-velocity model of a bubbly fluid (with incompressible liquid phase) at small volume concentration of gas bubbles (Zh. Prikl. Tekh. Fiz. 1960 York, 1998). These models are obtained for special types of the function W ( ,˙ ). The group classification separates these models in 10 different classes. Optimal systems of subalgebras are constructed for all models. The knowledge of optimal systems of admitted subalgebras allows constructing essentially different invariant solutions.

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Invariant and Partially Invariant Solutions of the Green-Naghdi Equations

Cited by 11 publications

References 5 publications

Invariant solutions of the special model of fluids with internal inertia

Invariant solutions of the special model of fluids with internal inertia

Applications of Group Analysis to the Three-Dimensional Equations of Fluids with Internal Inertia

Group classification of one‐dimensional equations of fluids with internal inertia

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