Integrating the Kadomtsev-Petviashvili Equation in the 1+3 Dimensions VIA the Generalised Monge-Ampère Equation: An Example of Conditioned Painlevé Test

ON THE BOUSSINESQ HIERARCHY

A new sequence of nonlinear evolution systems satisfying the zero curvature property is constructed, by using the invariant singularity analysis. All these systems are completely integrable and a pseudo-potential (linearization) is explicitly determined for each of them. The second system of the sequence is the Broer-Kaup system, which, as is well known, corresponds to the higher order Boussinesq approximation in describing shallow water waves.

Symmetry reduction of a model in spherical symmetry for benign tumor

A PDEs system, describing the expansive growth of a benign tumor and the phe- nomenon of encapsulation, is studied via a group analysis approach. A weak equiv- alence classi¯cation is obtained and the original PDEs system is reduced to an ODEs system. Numerical simulations are performed both for ODEs and PDEs, which turn out to be in perfect agreement between each other, showing a realistic enough description of the biological process.

A group analysis via weak equivalence transformations for a model of tumor encapsulation

A symmetry reduction of a PDEs system, describing the expansive growth of a benign tumour, is obtained via a group analysis approach. The presence in the model of three arbitrary functions suggests the use of Lie symmetries by using the weak equivalence transformations. An invariant classification is given which allows us to reduce the initial PDEs system to an ODEs system. Numerical simulations show a realistic enough description of the physical process.

A SUBCRITICAL BIFURCATION FOR A NONLINEAR REACTION–DIFFUSION SYSTEM

In this paper the mechanism of pattern formation for a reaction-diffusion system with nonlinear diffusion terms is investigated. Through a linear stability analysis we show that the cross-diffusion term allows the pattern formation. To predict the form and the amplitude of the pattern we perform a weakly nonlinear analysis. In the supercritical case the Stuart-Landau equation is found, which rules the evolution of the amplitude of the most unstable mode. With the increasing distance from the bifurcation value of the cross-diffusion parameter, the weakly nonlinear analysis fails and a Fourier–Galerkin approach is adopted. In the subcritical case the weakly nonlinear analysis must be pushed u…

Vermeir, René; Eebben, Maurits; Fagel, Raymond (eds.) (2011). Agentes e identidades en movimiento: España y los Países Bajos, siglos XVI-XVIII

Vermeir, René; Eebben, Maurits; Fagel, Raymond (eds.) (2011). Agentes e identidades en movimiento: España y los Países Bajos, siglos XVI-XVIII. Madrid: Sílex Ediciones, 464 p.