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Theoretical investigation of the nonlinear propagation and modulational instability (MI) of the dust acoustic (DA) waves (DAWs) in an unmagnetized electron depleted dusty plasma (containing opposite polarity warm dust grains and…
We demonstrate the existence of two species of stable bright solitons, fundamental and dipole ones, in one-dimensional self-defocusing nonlocal media, with the local value of nonlinearity coefficient having one or several minima and growing…
Dark solitons of ultracold bosons in the vicinity of the Mott-insulator--superfluid phase transition are studied. Making use of the Gutzwiller ansatz we have found antisymmetric eigenstates corresponding to standing solitons, as well as…
We theoretically study bright and dark solitons in an experimentally relevant hybrid system characterized by strong light-matter coupling. We find that the corresponding two-component model supports a variety of coexisting moving solitons…
It is an open fundamental question how the classical appearance of our environment arises from the underlying quantum many-body theory. We propose that phenomena involved in the quantum-to-classical transition can be probed in collisions of…
A theoretical investigation of the modulational instability (MI) of dust-acoustic waves (DAWs) by deriving a nonlinear Schr\"{o}dinger equation in an electron depleted opposite polarity dusty plasma system containing non-extensive positive…
We study on rational solutions on nonzero background of coupled Sasa-Satsuma equations through Darboux transformation method, which take into account third order dispersion, the term with self-frequency shift, and the term describing…
The phenomenon of dynamical localization of matter wave solitons in optical lattices is first demonstrated and the conditions for its existence are discussed. In addition to the trapping linear periodic potential we use a periodic…
Modulational instabilities play a key role in a wide range of nonlinear optical phenomena, leading e.g. to the formation of spatial and temporal solitons, rogue waves and chaotic dynamics. Here we experimentally demonstrate the existence of…
The properties of the localized states of a two component Bose-Einstein condensate confined in a nonlinear periodic potential [nonlinear optical lattice] are investigated. We reveal the existence of new types of solitons and study their…
This article discusses the existence of solitary electromagnetic waves trapped in a self-generated Langmuir wave and embedded in an infinitely long circularly polarized electromagnetic wave propagating through a plasma. From the…
We present a brief overview of the basic concepts of the soliton stability theory and discuss some characteristic examples of the instability-induced soliton dynamics, in application to spatial optical solitons described by the NLS-type…
We develop a nonlinear theory of soliton-induced waveguides that describes a finite-amplitude probe beam guided by a spatial dark soliton in a saturable nonlinear medium. We suggest an effective way to control the interaction of these…
We study various properties of the soliton solutions of the modified regularized long-wave equation. This model possesses exact one- and two-soliton solutions but no other solutions are known. We show that numerical three-soliton…
We unveil the relation between the linear Anderson localisation process and nonlinear modulation instability. Anderson localised modes are formed in certain temporal intervals due to the random background noise. Such localised modes seed…
The formation of unstaggered localized modes in dynamical lattices can be supported by the interplay of discreteness and nonlinearity with a finite relaxation time. In rapidly responding nonlinear media, on-site discrete solitons are…
Compact white dwarf (WD) binaries are important sources for space-based gravitational-wave (GW) observatories, and an increasing number of them are being identified by surveys like ZTF. We study the effects of nonlinear dynamical tides in…
We study how dark solitons, i.e. solutions of one-dimensional single-particle nonlinear time-dependent Schr\"odinger equation, emerge from eigenstates of a linear many-body model of contact interacting bosons moving on a ring, the…
We introduce a model for spatiotemporal modelocking in multimode fiber lasers, which is based on the (3+1)-dimensional cubic-quintic complex Ginzburg-Landau equation (cGLE) with conservative and dissipative nonlinearities and a…
A simulation study is performed to investigate the dynamics of coupled Langmuir waves (LWs) and ion-acoustic waves (IAWs) in an unmagnetized plasma. The effects of dispersion due to charge separation and the density nonlinearity associated…