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Oscillons are spatially stationary, quasi-periodic solutions of nonlinear field theories seen in settings ranging from granular systems, low temperature condensates and early universe cosmology. We describe a new class of oscillon in which…
We present a generalized (2+1)-dimensional Boussinesq equation, including two cases which are called the plus Boussinesq equation and the minus one. To investigate these equations, we apply the $\bar{\partial}$ approach to a coupled…
The generalized perturbative reduction method is used to find the two-component vector breather solution of the Born-Infeld equation $ U_{tt} -C U_{zz} = - A U_{t}^{2} U_{zz} - \sigma U_{z}^{ 2} U_{tt} + B U_{z} U_{t} U_{zt} $. It is shown…
We present a two-parameter family of exactly solvable quantum many-body systems in one spatial dimension containing the Lieb-Liniger model of interacting bosons as a particular case. The principal building block of this construction is the…
We introduce a generalized Gross-Pitaevskii equation that provides a nonlinear framework for studying two-dimensional (2D) attractive Bose systems. Its defining feature is the logarithmic density dependence of the coupling constant, which…
The wave equation with energy critical sources and nonlinear damping defined on a 3D bounded domain is considered. It is shown that the resulting dynamical system admits a global attractor. Under the additional assumption of strong…
We consider solutions of the $2\times 2$ matrix Hamiltonian of physical systems within the context of the asymptotic iteration method. Our technique is based on transformation of the associated Hamiltonian in the form of the first order…
The $D$-dimensional Smorodinsky-Winternitz system, proposed some years ago by Evans, is re-examined from an algebraic viewpoint. It is shown to possess a potential algebra, as well as a dynamical potential one, in addition to its known…
We present a pair of symmetric formulations of the matter sector of the stationary effective action of heterotic string theory that arises after the toroidal compactification of d dimensions. The first formulation is written in terms of a…
Waves with different symmetries exist in two-component Bose-Einstein condensates (BECs) whose dynamics is described by a system of coupled Gross-Pitaevskii (GP) equations. A first type of waves corresponds to excitations for which the…
Nonlinear supersymmetry is used to compute the general form of the effective D-brane action in type I string theory compactified to four dimensions in the presence of internal magnetic fields. In particular, the scalar potential receives…
We study half-space linear kinetic equations with general boundary conditions that consist of both given incoming data and various type of reflections, extending our previous work [LLS14] on half-space equations with incoming boundary…
We find a class of analytic solutions in open bosonic string field theory, parametrized by the chiral copy of higher spin algebra in $AdS_3$. The solutions are expressed in terms of the generating function for the products of Bell…
We generalize a family of Lagrangians with values in the Poincar\'e group ISO(d-1,1), which contain the description of spinning strings in flat (d-1)+1 dimensions, by including symmetric terms in the world-sheet coordinates. Then, by…
We consider the cubic nonlinear Schr\"{o}dinger equation in two space dimensions with an attractive potential. We study the asymptotic stability of the nonlinear bound states, i.e. periodic in time localized in space solutions. Our result…
We study a 1D semilinear wave equation modeling the dynamic of an elastic string interacting with a rigid substrate through an adhesive layer. The constitutive law of the adhesive material is assumed elastic up to a finite critical state,…
We study the Riemann geometric approach to be aimed at unifying soliton systems. The general two-dimensional Einstein equation with constant scalar curvature becomes an integrable differential equation. We show that such Einstein equation…
We study soliton dynamics in a system of two linearly coupled discrete nonlinear Schr\"odinger equations, which describe the dynamics of a two-component Bose gas, coupled by an electromagnetic field, and confined in a strong optical…
Ultracold condensates provide a unique platform for exploring soliton physics. Motivated by the recent experiments realizing the sine-Gordon model in a split one-dimensional (1D) BEC, we demonstrate that this system naturally supports…
We study bosonic string theory in a gravitational background. We show that either left-movers or right-movers are the only background independent non-perturbative solutions of the field equations for an arbitrary static metric. They are…