Related papers: High-order Rogue Waves in Vector Nonlinear Schr\"o…
A prototypical example of a rogue wave structure in a two-dimensional model is presented in the context of the Davey-Stewartson~II (DS~II) equation arising in water waves. The analytical methodology involves a Taylor expansion of an…
We investigate the nonisospectral effects of a semi-discrete nonlinear Schr\"{o}dinger equation, which is a direct integrable discretisation of its continuous counterpart. Bilinear form and double casoratian solution of the equation are…
In this work, we numerically consider the initial value problem for nonlinear Schr\"odinger (NLS) type models arising in the physics of ultracold boson gases, with generic Gaussian wavepacket initial data. The corresponding Gaussian's width…
A specific, genuinely three-dimensional mechanism of rogue wave formation, in a late stage of the modulational instability of a perturbed Stokes deep-water wave, is recognized through numerical experiments. The simulations are based on…
We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schroedinger equations. We derive a nonlinear dispersion relation.…
The formation of coherent structures in noise driven phenomena and in Turbulence is a complex and fundamental question. A particulary important structure is the so-called Rogue Wave (RW) that arises as the sudden appearance of a localized…
The mechanism of a rogue water wave is still unknown. One popular conjecture is that the Peregrine wave solution of the nonlinear Schr\"odinger equation (NLS) provides a mechanism. A Peregrine wave solution can be obtained by taking the…
The nonlinear Schrodinger equation is a classical integrable equation which contains plenty of significant properties and occurs in many physical areas. However, due to the difficulty of solving this equation, in particular in high…
The rogue waves in a resonant erbium-doped fibre system governed by a coupled system of the nonlinear Schr\"odinger equation and the Maxwell-Bloch equation (NLS-MB equations) are given explicitly by a Taylor series expansion about the…
We construct rogue wave solutions of a fifth-order nonlinear Schr\"odinger equation on the Jacobian elliptic function background. By combining Darboux transformation and the nonlinearization of spectral problem, we generate rogue wave…
We have studied the Rogue wave existence and propagation in Ion-acoustic mode for the highly energetic case using kappa distributed electrons in accordance with the Korteweg de Vries equation that is modified KdV and extended KdV equation.…
We construct higher order rogue wave solutions for the Gerdjikov-Ivanov equation explicitly in term of determinant expression. Dynamics of both soliton and non-soliton solutions is discussed. A family of solutions with distinct structures…
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…
In this essay we give an overview on the problem of rogue or freak wave formation in the ocean. The matter of the phenomenon is a sporadic occurrence of unexpectedly high waves on the sea surface. These waves cause serious danger for…
We advance a statistical theory of extreme event emergence in random nonlinear wave systems with self-similar intermediate asymptotics. We show, within the framework of a generic (1 + 1)D nonlinear Schrodinger equation with linear gain,…
Rogue waves are extreme and rare fluctuations of the wave field that have been discussed in many physical systems. Their presence substantially influences the statistical properties of an incoherent wave field. Their understanding is…
Within the (2 + 1)-dimensional Korteweg-de Vries equation framework, new bilinear Backlund transformation and Lax pair are presented based on the binary Bell polynomials and gauge transformation. By introducing an arbitrary function, a…
Some years ago, Chen, Pelinovsky, and White claimed existence of certain solutions of the nonlinear Schr\"odinger equation for modelling rogue waves [arXiv: 1909.08165v1 (2019)]. It is the aim of this Comment to outline that this claim is…
Using the inverse spectral theory of the nonlinear Schrodinger (NLS) equation we correlate the development of rogue waves in oceanic sea states characterized by the JONSWAP spectrum with the proximity to homoclinic solutions of the NLS…
Nonlinear dynamics of surface gravity waves trapped by an opposing jet current is studied analytically and numerically. For wave fields narrowband in frequency but not necessarily with narrow angular distributions the developed asymptotic…