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We study waves on infinite one-dimensional lattices of particles that each interact with all others through power-law forces $F \sim r^{-\beta}$. The inverse-cube case corresponds to Calogero-Moser systems, which are well known to be…
The interaction of a solitary wave front with an interface formed by two strongly-nonlinear non-cohesive granular lattices displays rich behaviour, characterized by the breakdown of continuum equations of motion in the vicinity of the…
We characterize the soliton solutions of the nonlinear Schroedinger equation on the half line with linearizable boundary conditions. Using an extension of the solution to the whole line and the corresponding symmetries of the scattering…
Quantitative thermodynamical, dynamical and magnetic properties of the solar and stellar plasmas are obtained by interpreting their emergent non-polarized and polarized spectrum. This inference requires the selection of a set of spectral…
We present experiments performed in a recirculating fiber loop in which we realize the single-shot observation of the space and time interaction of two and three bright solitons. The space-time evolutions observed in experiments provide…
Interactions between solitons and the coherent oscillation structures generated by localized disturbances via modulational instability are studied within the framework of the focusing nonlinear Schrodinger equation. Two main interaction…
Nonlocal integrable partial differential equations possessing a spatial or temporal reflection have constituted an active research area for the past decade. Recently, more general classes of these nonlocal equations have been proposed,…
We introduce a new class of self-sustained states, which may exist as single solitons or form multisoliton clusters, in driven passive cylindrical microresonators. Remarkably, such states are stabilized by the radiation they emit, which…
The defocusing nonlinear Schr\"odinger (NLS) equation has no the modulational instability, and was not found to possess the rogue wave (RW) phenomenon up to now. In this paper, we firstly investigate some novel nonlinear wave structures in…
We study a parametrically forced nonlinear Schr\"odinger (PFNLS) equation, driven by multiplicative translation-invariant noise. We show that a solitary wave in the stochastic equation is orbitally stable on a timescale which is exponential…
The hot and diffuse nature of the Sun's extended atmosphere allows it to persist in non-equilibrium states for long enough that wave-particle instabilities can arise and modify the evolution of the expanding solar wind. Determining which…
When solitary waves are characterized as homoclinic orbits of a finite-dimensional Hamiltonian system, they have an integer-valued topological invariant, the Maslov index. We are interested in developing a robust numerical algorithm to…
The dynamics of ultralight dark matter with non-negligible self-interactions are determined by a nonlinear Schr\"odinger equation rather than by the Vlasov equation of collisionless particles. This leads to wave-like effects, such as…
We study solitons in three dimensional non-commutative scalar field theory at infinite non-commutativity parameter. We find the metric on the relative moduli space of all solitons of the form |n><n| and show that it is Kahler. We then find…
The nature of transverse instabilities to dark solitons and dispersive shock waves for the (2+1)-dimensional defocusing nonlinear Schrodinger equation / Gross-Pitaevskii (NLS / GP) equation is considered. Special attention is given to the…
Spectra observed with the Ultraviolet and Visual Echelle Spectrograph (UVES) on the European Southern Observatory's VLT exhibit long-range wavelength distortions. These distortions impose a systematic error on high-precision measurements of…
We consider the nonlinear Schr{\"o}dinger equation (NLSE) in 1+1 dimension with scalar-scalar self interaction $\frac{g^2}{\kappa+1} (\psi^\star \psi)^{\kappa+1}$ in the presence of the external forcing terms of the form $r e^{-i(kx +…
An analysis of discrete systems is important for understanding of various physical processes, such as excitations in crystal lattices and molecular chains, the light propagation in waveguide arrays, and the dynamics of Bose-condensate…
The long-time asymptotics is analyzed for finite energy solutions of the 1D Schr\"odinger equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group U(1). For initial states close to…
We investigate the propagation of an ultrashort optical pulse using Fokas-Lenells equation (FLE) under varying dispersion, nonlinear effects and perturbation. Such a system can be said to be under soliton management (SM) scheme. At first,…