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We study nonlocal bright solitons subject to external spatially nonuniform potentials. If the potential is slowly varying on the soliton scale, we derive analytical soliton solutions behaving like Newtonian particles. If the potential has…
We describe a general N-solitonic solution of the focusing NLSE in the presence of a condensate by using the dressing method. We give the explicit form of one- and two- solitonic solutions and study them in detail. We distinguish a special…
The cosmological two brane model is discussed in detail. An elegant method for deriving the generalised non-linear equations for the interbrane distance is presented. These equations are used to identify equilibrium positions of the radion,…
A new nonlinear Schroedinger equation is obtained explicitly from the fractal Brownian motion of a massive particle with a complex-valued diffusion constant. Real-valued energy (momentum) plane wave and soliton solutions are found in the…
In this paper we study existence and orbital stability for solitary waves of the nonlinear Klein-Gordon equation. The energy of these solutions travels as a localized packet, hence they are a particular type of solitons. In particular we…
We compute electromagnetic wave propagation through the magnetosphere of a magnetar. The magnetosphere is modeled as the QED vacuum and a cold, strongly magnetized plasma. The background field and electromagnetic waves are treated…
We investigate the existence and propagation properties of all possible types of envelope soliton pulses in a birefringent optical fiber wherein the light propagation is governed by two coupled nonlinear Schrodinger equations with coherent…
We explore a prototypical two-dimensional model of the nonlinear Dirac type and examine its solitary wave and vortex solutions. In addition to identifying the stationary states, we provide a systematic spectral stability analysis,…
We investigate the presence of soliton solutions in some classes of nonlinear partial differential equations, namely generalized Korteweg-de Vries-Burgers, Korteveg-de Vries-Huxley, and Korteveg-de Vries-Burgers-Huxley equations, which…
In this paper we construct a new solution which represents Pollard-like three-dimensional nonlinear geophysical internal water waves. The Pollard-like solution includes the effects of the rotation of Earth and describes the internal water…
We develop a numerical a framework to study phoretic particle dynamics in two dimensions. The particles are modeled as chemically active rigid circles, which can emit or absorb a solute into surrounding fluid. The interaction between…
The helicon waves exhibit varying characters depending on plasma parameters, geometry, and wave numbers. Here we elucidate an intrinsic multi-scale property embodied by the combination of dispersive effect and nonlinearity. The extended…
We present dynamic equations for two dimensional closed surfaces and analytically solve it for some simplified cases. We derive final equations for surface normal motions by two different ways. The solution of the equations of motions in…
We present the theory of non-stationary normal forms for uniformly contracting smooth extensions with sufficiently narrow Mather spectrum. We give coherent proofs of existence, (non)uniqueness, and a description of the centralizer results.…
Using the ``composite harmonic mapping method," we construct exact solutions for cylindrically symmetric gravitational and electromagnetic waves within the Einstein-Maxwell system, focusing on the conversion dynamics between these types of…
We study classical energy-momentum ($E$-$m$) diagrams for rotational motion of dipolar asymmetric top molecules in strong external fields. Static electric fields, nonresonant linearly polarized laser fields, and collinear combinations of…
We consider the one-dimensional dynamics of nonlinear non-dispersive waves. The problem can be mapped onto a linear one by means of the hodograph transform. We propose an approximate scheme for solving the corresponding Euler-Poisson…
We investigate symmetry-breaking phenomena in semilinear elliptic systems on the unit ball in $\mathbb{R}^3$, focusing on the emergence of non-radial solution branches with prescribed spatial and internal symmetries. Extending previous…
We formulate and explore a generic continuum model of a polarizable active layer with neo-Hookean elasticity and chemo-mechanical interactions. Homogeneous solutions of the model equations exhibit a stationary long-wave instability when the…
The evaluation of collective modes is fundamental in the analysis of molecular dynamics simulations. Several methods are available to extract that information, i.e normal mode analysis, principal component and spectral analysis of…