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A note on poroacoustic traveling waves under Darcy's law: Exact solutions

P. M. Jordan, J. K. Fulford (2011)

Applications of Mathematics

A mathematical analysis of poroacoustic traveling wave phenomena is presented. Assuming that the fluid phase satisfies the perfect gas law and that the drag offered by the porous matrix is described by Darcy's law, exact traveling wave solutions (TWS)s, as well as asymptotic/approximate expressions, are derived and examined. In particular, stability issues are addressed, shock and acceleration waves are shown to arise, and special/limiting cases are noted. Lastly, connections to other fields are...

Application of a center manifold theory to a reaction-diffusion system of collective motion of camphor disks and boats

Shin-Ichiro Ei, Kota Ikeda, Masaharu Nagayama, Akiyasu Tomoeda (2014)

Mathematica Bohemica

Unidirectional motion along an annular water channel can be observed in an experiment even with only one camphor disk or boat. Moreover, the collective motion of camphor disks or boats in the water channel exhibits a homogeneous and an inhomogeneous state, depending on the number of disks or boats, which looks like a kind of bifurcation phenomena. In a theoretical research, the unidirectional motion is represented by a traveling wave solution in a model. Hence it suffices to investigate a linearized...

Applications of an extended $(G^{'} / G)$ -expansion method to find exact solutions of nonlinear PDEs in mathematical physics.

Zayed, E.M.E., Al-Joudi, Shorog (2010)

Mathematical Problems in Engineering

Applications of the new compound Riccati equations rational expansion method and Fan's subequation method for the Davey-Stewartson equations.

Zedan, Hassan (2010)

Boundary Value Problems [electronic only]

Asymptotic and numerical description of the kink/antikink interaction.

Omel'yanov, Georgii A., Segundo-Caballero, Israel (2010)

Electronic Journal of Differential Equations (EJDE) [electronic only]