Related papers: Some breathers and multi-breathers for FPU-type ch…
We consider localized solutions of variants of the semilinear curl-curl wave equation $s(x) \partial_t^2 U +\nabla\times\nabla\times U + q(x) U \pm V(x) |U|^{p-1} U = 0$ for $(x,t)\in \mathbb{R}^3\times\mathbb{R}$ and arbitrary $p>1$.…
In this work, a rigorous proof of the nonexistence of breather solutions for NLS equations is presented. By using suitable virial functionals, we are able to characterize the nonexistence of breather solutions, different from standing…
Metamaterials, i.e., artificially structured ("synthetic") media comprising weakly coupled discrete elements, exhibit extraordinary properties and they hold a great promise for novel applications including super-resolution imaging,…
Nonlinear networks can host spatially compact time periodic solutions called compact breathers. Such solutions can exist accidentally (i.e. for specific nonlinear strength values) or parametrically (i.e. for any nonlinear strength). In this…
We obtain an exact solution for the breather lattice solution of the modified Korteweg-de Vries (MKdV) equation. Numerical simulation of the breather lattice demonstrates its instability due to the breather-breather interaction. However,…
Discrete breathers, or intrinsic localized modes, are spatially localized, time--periodic, nonlinear excitations that can exist and propagate in systems of coupled dynamical units. Recently, some experiments show the sighting of a form of…
We discuss the existence of breathers and lower bounds on their power, in nonlinear Schr\"odinger lattices with nonlinear hopping. Our methods extend from a simple variational approach to fixed point arguments, deriving lower bounds for the…
We consider Maxwell's equations for Kerr-type optical materials, which are magnetically inactive and have a nonlinear response to electric fields. This response consists of a linear plus a cubic term, which are both inhomogeneous with…
We study the properties of moving breathers in a bent DNA-related model with short range interaction, due to the stacking of the base pairs, and long range interaction, due to the finite dipole moment of the bonds within each base pair. We…
In this work, we revisit the question of stability of multibreather configurations, i.e., discrete breathers with multiple excited sites at the anti-continuum limit of uncoupled oscillators. We present two methods that yield quantitative…
We construct lattice Hamiltonians with homogeneous interaction potentials which allow for explicit breather solutions. Especially we obtain exponentially localized solutions for $d$-dimensional lattices with $d=2,3$.
We review recent studies about quantum discrete breathers. We describe their basic properties in comparison with their classical counterparts, and the ways they may be addressed theoretically in different quantum lattice models including…
We consider the nonlinear Schr\"odinger equation with non-local derivatives in a two-dimensional periodic domain. For certain orders of derivatives, we find a new type of breather solution dominating the field evolution at low nonlinearity…
We introduce a one dimensional parity-time (PT)-symmetric nonlinear magnetic metamaterial consisted of split ring dimers having both gain and loss. When nonlinearity is absent we find a transition between an exact to a broken PT-phase; in…
We consider multidimensional quadratic BSDEs with bounded and unbounded terminal conditions. We provide sufficient conditions which guarantee existence and uniqueness of solutions. In particular, these conditions are satisfied if the…
We study experimentally and numerically the existence and stability properties of discrete breathers in a periodic nonlinear electric line. The electric line is composed of single cell nodes, containing a varactor diode and an inductor,…
Intrinsic localized modes or discrete breathers are investigated by molecular dynamics simulations in free-standing graphene. Discrete breathers are generated either through thermal quenching of the graphene lattice or by proper…
The unique geometry of the two-dimensional tripartite Kagome lattice is responsible for shaping diverse families of spatially localized and time-periodic nonlinear modes known as discrete breathers. We state conditions for the existence of…
Whereas there exists a mathematical proof for one--site breathers stability, and an unpublished one for two--sites breathers, the methods for determining the stability properties of multibreathers rely in numerical computation of the…
Analytical solutions for (1+1)D surface fundamental solitons in thermal nonlinear media are obtained. The stationary position and the critical power of surface solitons are obtained using this analytical solutions. The analytical solutions…