Related papers: Vector rogue wave patterns of the multi-component …
In this paper, we construct a generalized Darboux transformation for nonlinear Schr\"odinger equation. The associated $N$-fold Darboux transformation is given both in terms of a summation formula and in terms of determinants. As…
The dynamics of two-component solitons is studied, analytically and numerically, in the framework of a system of coupled extended nonlinear Schr\"odinger equations, which incorporate the cross-phase modulation,…
The generation of rogue waves is investigated via a nonlocal nonlinear Schrodinger (NLS) equation. In this system, modulation instability is suppressed and is usually expected that rogue wave formation would also be limited. On the…
We considered the modulational instability of continuous-wave backgrounds, and the related generation and evolution of deterministic rogue waves in the recently introduced parity-time (PT)-symmetric system of linearly-coupled nonlinear…
In this letter,the designable integrability(DI) of the variable coefficient derivative nonlinear Schr\"odinger equation (VCDNLSE) is shown by construction of an explicit transformation which maps VCDNLSE to the usual derivative nonlinear…
The rogue wave solutions (rational multi-breathers) of the nonlinear Schrodinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5…
We investigate higher-order breathers of the cubic nonlinear Schr\"odinger equation on an elliptic background. We find that, beyond first-order, any arbitrarily constructed breather is a single-peaked solitary wave on a disordered…
We study a variable-coefficient nonlinear Schr\"odinger (vc-NLS) equation with higher-order effects. We show that the breather solution can be converted into four types of nonlinear waves on constant backgrounds including the multi-peak…
The long wave-short wave model describes the interaction between the long wave and the short wave. Exact higher-order rational solution expressed by determinants is calculated via the Hirota's bilinear method and the KP hierarchy reduction.…
The the mixed Chen-Lee-Liu derivative nonlinear Schr\"odinger equation (CLL-NLS) can be considered as simplest model to approximate the dynamics of weakly nonlinear and dispersive waves, taking into account the self-steepnening effect…
Considering the importance of ever-increasing interest in exploring localized waves, we investigate a generalized (3+1)-dimensional Hirota-Satsuma-Ito equation describing the unidirectional propagation of shallow-water waves and perform…
This paper proposes an Adaptive-Growth Randomized Neural Network (AG-RaNN) method for computing multivalued solutions of nonlinear first-order PDEs with hyperbolic characteristics, including quasilinear hyperbolic balance laws and…
General high-order rogue waves of the NLS-Boussinesq equation are obtained by the KP-hierarchy reduction theory. These rogue waves are expressed with the determinants, whose entries are all algebraic forms. It is found that the fundamental…
We present a study devoted to a detailed description of modulated rotating waves (MRW) in the magnetized spherical Couette system. The set-up consists of a liquid metal confined between two differentially rotating spheres and subjected to…
We present exact rational solution for a modified nonlinear Schr$\ddot{o}$dinger equation that takes into account quintic nonlinearity and nonlinear dispersion corrections to the cubic nonlinearity, which could be used to describe rogue…
General high-order rogue wave solutions for the (1+1)-dimensional Yajima-Oikawa (YO) system are derived by using Hirota's bilinear method and the KP-hierarchy reduction technique. These rogue wave solutions are presented in terms of…
We construct Darboux transformation of a coupled generalized nonlinear Schr\"odinger (CGNLS) equations and obtain exact analytic expressions of breather and rogue wave solutions. We also formulate the conditions for isolating these…
We study artificial neural networks with nonlinear waves as a computing reservoir. We discuss universality and the conditions to learn a dataset in terms of output channels and nonlinearity. A feed-forward three-layer model, with an…
We study a deformation of the nonlinear Schr\"odinger equation recently derived in the context of deformation of hierarchies of integrable systems. This systematic method also led to known integrable equations such as the Camassa-Holm…
Exact explicit rational solutions of two- and one- dimensional multicomponent Yajima-Oikawa (YO) systems, which contain multi-short-wave components and single long-wave one, are presented by using the bilinear method. For two-dimensional…