On a Boussinesq capillarity system: Hamiltonian reductions and associated quartic geometries. (English) Zbl 1290.35207

The authors deal with the nonlinear Boussinesq capillarity system which may be derived from the L. K. Antanovskii model [“Microscale theory of surface tension”, Phys. Rev. E. 54, 6285–6290 (1996)] in one case of one-parameter free-energy laws. The application of a quartic ansatz for the density distribution leads to Hamiltonian reductions associated with isopycnal geometries: in \(2+1\) dimension with time-modulated Cassini ovals and in \(3+1\) dimension with time-modulated “red blood cell” geometries [B. Angelov and I. M. Mladenov, in: Proceedings of the international conference on geometry, integrability and quantization, Varna, Bulgaria, 1999. Sofia: Coral Press Scientific Publishing. 27–46 (2000; Zbl 0970.92009)]. Thus it is shown that the considered nonlinear Boussinesq-type capillarity model system allows exact reduction to coupled Hamiltonian subsystems.


35Q35 PDEs in connection with fluid mechanics
35Q55 NLS equations (nonlinear Schrödinger equations)
76D45 Capillarity (surface tension) for incompressible viscous fluids
76A05 Non-Newtonian fluids


Zbl 0970.92009
Full Text: DOI


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