Related papers: Soliton on Unstable Condensate
We consider KdV-type equations with $C^1$ nonhomogeneous nonlinearities and small dispersion $\varepsilon$. The first result consists in the conclusion that, in the leading term with respect to $\varepsilon$, the solitary waves in this…
Physically relevant soliton solutions of the resonant nonlinear Schrodinger (RNLS) equation with nontrivial boundary conditions, recently proposed for description of uniaxial waves in a cold collisionless plasma, are considered in the…
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,…
In this paper, by means of similarity transformations we study exact analytical solutions for a generalized nonlinear Schr$\ddot{\mbox{o}}$dinger equation with variable coefficients. This equation appears in literature describing the…
Propagation of localized waves in a Fermi-Dirac distributed super dense matter at the presence of strong external magnetic fields is studied using the reductive perturbation method. Previous works indicate that localized waves break down in…
We use the inverse scattering transform and a diffusion approximation limit theorem to study the stability of soliton components of the solution of the nonlinear Schr\"{o}dinger and Korteweg-de Vries equations under random perturbations of…
Optical propagation and vortices in nonlinear media have been intensively studied in modern optical physics. In this paper, we establish constraints regarding the propagation constant and provide an existence theory and numerical…
It is well-known that third-order dispersion (TOD) never allows the continuous wave of any nonlinear Schroedinger (NLS) type system to experience modulational instability (MI). Remarkably, we demonstrate a new kind of MI induced by TOD with…
We consider the focusing $L^2$-supercritical Schr\"odinger equation in the exterior of a smooth, compact, strictly convex obstacle. We construct a solution behaving asymptotically as a solitary waves on $R^3$, as large time. When the…
We are interested in solutions of the nonlinear Klein-Gordon equation (NLKG) in $\mathbb{R}^{1+d}$, $d\ge1$, which behave as a soliton or a sum of solitons in large time. In the spirit of other articles focusing on the supercritical…
We study the convergence of solutions of the discrete nonlinear Klein-Gordon equation on an infinite lattice in the continuum limit, using recent tools developed in the context of nonlinear discrete dispersive equations. Our approach relies…
The data recorded in optical fiber [1] and in hydrodynamic [2] experiments reported the pioneering observation of nonlinear waves with spatiotemporal localization similar to the Peregrine soliton are examined by using nonlinear spectral…
In this paper we study the Nonlinear Schr\"odinger-Maxwell equations (NSM). We are interested to analyse the existence of solitons, namely of finite energy solutions which exhibit stability properties. This paper is divided in two parts. In…
We study the instability of standing waves for nonlinear Schr\"{o}dinger equations. Under a general assumption on nonlinearity, we prove that linear instability implies orbital instability in any dimension. For that purpose, we establish a…
In this paper we address the issue of stability for the near-inertial Pollard waves, as a model for the halocline in the region of the Arctic Ocean centered around the North Pole, derived in Puntini (2026). Adopting the short-wavelength…
We consider a coherently coupled nonlinear Schr\"odinger equation with modulated self-phase modulation, cross-phase modulation, and four-wave mixing nonlinearities and varying refractive index in anisotropic graded index nonlinear medium.…
In this paper, by considering the potential application in two mode nonlinear waves in nonlinear fibers under a certain case, we define a coupled nonlinear Schr\"odinger equation(called Frobenius NLS equation) including its Lax pair.…
We investigate the spectral stability of non-degenerate vector soliton solutions and the nonlinear stability of breather solutions for the coupled nonlinear Schrodinger (CNLS) equations. The non-degenerate vector solitons are spectrally…
We construct and discuss a semi-rational, multi-parametric vector solution of coupled nonlinear Schr\"odinger equations (Manakov system). This family of solutions includes known vector Peregrine solutions, bright-dark-rogue solutions, and…
A nonlinear Schr\"odinger equation with repulsive (defocusing) nonlinearity is considered. As an example, a system with a spatially varying coefficient of the nonlinear term is studied. The nonlinearity is chosen to be repelling except on a…