We analyze a system of reacting elements harmonically coupled to nearest neighbors in the continuum limit. An analytic solution is found for traveling waves. The procedure is used to find oscillatory as well as solitary waves. A comparison is made between exact solutions and solutions of the...

A class of one-dimensional, locally-nonlinear, dispersive Hamiltonians is defined, which includes both the sine Gordon and ø4 models. A transfer integral operator technique is used to investigate the classical statistical mechanics for this class, and several universality and scaling properties...

We propose a versatile variational method to investigate the spatio-temporal dynamics of one-dimensional magnetically-trapped Bose-condensed gases. To this end we employ a q-Gaussian trial wave-function that describes both the low- and the high-density limit of the ground state of a...

We study the dynamics of solitons in Bose–Einstein condensates (BECs) loaded into an optical lattice (OL), which is combined with an external parabolic potential. Chiefly, the one-dimensional (1D) case is considered. First, we demonstrate analytically that, in the case of the repulsive BEC,...

We describe a novel class of solitary waves in second-harmonic-generation models with competing quadratic and cubic nonlinearities. These solitary waves exist at a discrete set of values of the propagation constants, being embedded inside the continuous spectrum of the linear system (“embedded...

We examine how nonlinear dispersion relations (NLDR) can be used as a simple, universal algebraic tool to provide information for the localized, nonlinear solutions of PDE that model physical systems. Such scaling relations between width, amplitude and velocity are of great help for numerical...

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...

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...