Related papers: On Lorentz-invariant 2D equations admitting long-l…
We study steady solutions to the relativistic Boltzmann equation with hard-sphere interactions in a slab geometry. Under a spatial symmetry assumption in the transverse variables $x_2$ and $x_3$, the problem reduces to a one-dimensional…
We study the dynamics of two-dimensional (2D) localized modes in the nonlinear lattice described by the discrete nonlinear Schr\"{o}dinger (DNLS) equation, including a local linear or nonlinear defect. Discrete solitons pinned to the…
We investigate the presence of static solutions in models described by real scalar field in two-dimensional spacetime. After taking advantage of a procedure introduced sometime ago, we solve intricate nonlinear ordinary differential…
We show that integrable involutive maps, due to the fact they admit three integrals in separated form, can give rise to equations, which are consistent around the cube and which are not in the multiaffine form assumed in papers [1, 2].…
Two-place nonlocal systems have attracted many scientists' attentions. In this paper, two-place non-localities are extended to multi-place non-localities. Especially, various two-place and four-place nonlocal nonlinear Schrodinger (NLS)…
In this work we present nonlinear models in two-dimensional space-time of two interacting scalar fields in the Lorentz and CPT violating scenarios. We discuss the soliton solutions for these models as well as the question of stability for…
We study the local H\"older continuity of nonnegative solutions to doubly nonlinear equations by introducing a new technique that allows us to treat the cases where the equation is both singular and degenerate, up to specific Barenblatt…
We consider the defocusing cubic nonlinear Schr\"odinger equation (NLS) on the two-dimensional torus. The equation admits a special family of elliptic invariant quasiperiodic tori called finite-gap solutions. These are inherited from the…
Two-dimensional (2D) equations describing the nonlinear interaction between upper-hybrid and dispersive magnetosonic waves are presented. Nonlocal nonlinearity in the equations results in the possibility of existence of stable 2D nonlinear…
We consider steady solutions to the incompressible Euler equations in a two-dimensional channel with rigid walls. The flow consists of two periodic layers of constant vorticity separated by an unknown interface. Using global bifurcation…
We investigate two-dimensional neural fields as a model of the dynamics of macroscopic activations in a cortex-like neural system. While the one-dimensional case has been treated comprehensively by Amari 30 years ago, two-dimensional neural…
Existence, stability and dynamics of soliton complexes, centered at the site of a single transverse link connecting two parallel 2D (two-dimensional) lattices, are investigated. The system with the on-site cubic self-focusing nonlinearity…
In the present work, we generalize earlier considerations for intrinsic localized modes consisting of a few excited sites, as developed in the one-component discrete nonlinear Schrodinger equation model, to the case of two-component…
We study nonlinear excitations described by DNLS-type equations with so-called competing nonlinearities. These are the nonlinearities that consist of two power terms with coefficients of different sign. A key feature of these models is the…
The 2-matrix models can be defined in a setting more general than polynomial potentials, namely, the semiclassical matrix model. In this case, the potentials are such that their derivatives are rational functions, and the integration paths…
In this work we investigate the presence of scalar field models supporting kink solutions with logarithmic tails, which we call super long-range structures. We first consider models with a single real scalar field and associate the…
We investigate the evolutionary aspects of some integrable soliton models whose Lagrangians are derived from the pullback of a volume-form to a two-dimensional target space. These models are known to have infinitely many conserved…
The existence of nonzero localised periodic solutions for general one-dimensional discrete nonlinear Klein-Gordon systems with convex on-site potentials is proved. The existence problem of localised solutions is expressed in terms of a…
This work deals with models described by three real scalar fields in one spatial dimension. We study the case where two of the three fields engender kinematical modifications, which respond as geometrical constrictions, that can be used to…
We use ideas on integrability in higher dimensions to define Lorentz invariant field theories with an infinite number of local conserved currents. The models considered have a two dimensional target space. Requiring the existence of…