Antisolitons traveling on the surface of a nucleus are shown to generate highly deformed shapes. The dynamics is based on solutions of the non-linear Korteweg-de Vries (KdV) equation. The theory is used to model the onset of nuclear fission. Aspects of the dynamics, its relation to fluid...

We introduce an elastic beam Bernoulli–Euler model for the axoneme (cytoskeletal inner core of eukaryotic cells appendages) whose dynamics is controlled by internally generated torques at the inflexion points of the beam. We calculate the geometrical and the mechanical parameters of the...

We develop a geometrical approach for the relative sliding (shear) between filaments in a bundle subjected to bending and twisting deformations, with applications to motility in flagellated cells. Particular examples for helical and toroidal shapes, and combinations of these, are discussed. The...

We use a multi-scale similarity analysis which gives specific relations between the velocity, amplitude and width of localized solutions of nonlinear differential equations, whose exact solutions are generally difficult to obtain.

We introduce a qualitative similarity analysis, which yields relations between the geometry and kinematics of traveling localized solutions, associated to certain non-linear equations. This method predicts the existence of solitons, compactons, dublets, triplets, as well as other non-linear...

We generalize the one-dimensional KdV equation for an inviscid incompressible irrotational fluid layer with free surface, finite depth, and finite boundary conditions. We study the nonlinear dynamics of a fluid of arbitrary depth in a bounded domain. By introducing a special relation between the...

We study the dynamics of atomic Bose–Einstein condensates (BECs), when the quadrupole mode is excited. Within the Thomas–Fermi approximation, we derive an exact first-order system of differential equations that describes the parameters of the BEC wave function. Using perturbation theory...

In this short communication we study compactons in the setting of discrete nonlinear Klein–Gordon (DNKG) chains. The temporal and spatial dependences of the solutions are separated resulting in an array of coupled nonlinear algebraic equations for the spatial dependence and an ordinary...

Square barrier initial potentials for the Ablowitz–Ladik (AL) lattice are considered, both in the single component as well as in the vector (Manakov) case. We determine the threshold condition for creating solitons with such initial conditions in these integrable, discrete versions of the...

We revisit the topic of the existence and azimuthal modulational stability of solitary vortices (alias vortex solitons) in the two-dimensional (2D) cubic–quintic nonlinear Schrödinger equation. We develop a semi-analytical approach, assuming that the vortex soliton is relatively narrow, which...