Related papers: Optical Kerr spatiotemporal dark extreme waves
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 +…
The Kadomtsev--Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold…
It is demonstrated the existence of multidimensional matter-wave solitons in a crossed optical lattice (OL) with linear OL in the $x-$direction and nonlinear OL (NOL) in the $y-$direction, where the NOL can be generated by a periodic…
From inherent non-linearity two gravitational waves, unless they are unidirectional, fail to satisfy a superposition law. They collide to develop a new spacetime carrying the imprints of the incoming waves. Same behaviour is valid also for…
The investigation employed the reductive perturbation approach to study the nonlinear propagation of shear Alfvenic waves in an electron-positron (EP) plasma medium. Utilizing the solitary wave solution of the derivative nonlinear…
The long-time asymptotics is analyzed for finite energy solutions of the 1D discrete Schr\"odinger equation coupled to a nonlinear oscillator. The coupled system is invariant with respect to the phase rotation group. For initial states…
The various patterns of internal solitary wave interactions are complex phenomena in the ocean, susceptible to the influence of shear flow and density distributions. Satellite imagery serves as an effective tool for investigating these…
The dynamics of nonlinear waves with controllable dispersion, nonlinearities, and background continues to be an exciting line of research in recent years. In this work, we focus to investigate an integrable (3+1)-dimensional nonlinear model…
We present a novel computational methodology for solving the scalar nonlinear Helmholtz equation (NLH) that governs the propagation of laser light in Kerr dielectrics. The methodology addresses two well-known challenges in nonlinear optics:…
The two-dimensional evolution of perturbed long weakly-nonlinear surface plane, ring, and hybrid waves, consisting, to leading order, of a part of a ring and two tangent plane waves, is modelled numerically within the scope of the 2D…
A concept of semiclassically concentrated solutions is formulated for the multidimensional nonlinear Schr\"odinger equation (NLSE) with an external field. These solutions are considered as multidimensional solitary waves. The center of mass…
We establish the full asymptotic stability of solitary wave solutions for the 1D focusing cubic Schr\"odinger equation on the line under small perturbations in weighted Sobolev spaces, building upon our results in [58]. The proof integrates…
We re-derive the equation for vertical hydrodynamical equilibrium of stationary thin and slim accretion disks in the Kerr spacetime. All the previous derivations have been unsatisfactory, yielding unphysical singularities. Our equation is…
An exact solitary wave solution is presented for the nonlinear Schrodinger equation governing the propagation of pulses in optical fibers including the effects of second, third and fourth order dispersion. The stability of this soliton-like…
Rogue waves in the nonlocal PT-symmetric nonlinear Schrodinger (NLS) equation are studied by Darboux transformation. Three types of rogue waves are derived, and their explicit expressions in terms of Schur polynomials are presented. These…
We prove the existence of solitary waves in the KdV limit of two-dimensional FPU-type lattices using asymptotic analysis of nonlinear and singularly perturbed integral equations. In particular, we generalize the existing results by…
We determine conditions under which a generic gauge invariant nonautonomous and inhomogeneous nonlinear partial differential equation in the two-dimensional space-time continuum can be transform into standard autonomous forms. In addition…
We justify rigorously the convergence of the amplitude of solutions of Nonlinear-Schr\"odinger type Equations with non zero limit at infinity to an asymptotic regime governed by the Korteweg-de Vries equation in dimension 1 and the…
We construct vector rogue wave solutions of the two-dimensional two coupled nonlinear Schr\"{o}dinger equations with distributed coefficients, namely diffraction, nonlinearity and gain parameters through similarity transformation technique.…
In this paper we study the solitary waves for the coupled Schr\"odinger - Maxwell equations in three-dimensional space. We prove the existence of a sequence of radial solitary waves for these equations with a fixed $L^2$ norm. We study the…