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...

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.

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...

In the present communication, we derive averaging equations for nonlinear Schrödinger settings with periodic as well as ergodic random potentials. Our case examples are motivated by recent experimentally accessible applications in soft-condensed matter, as well as in optical physics. Particular...

We explore spatially extended dynamical states in the discrete nonlinear Schrödinger lattice in two- and three-dimensions, starting from the anti-continuum limit. We first consider the “core” of the relevant states (either a two-dimensional “tile” or a three-dimensional “stone”),...