Related papers: Rogue waves in the massive Thirring model
Based on the soliton solution on a continuous wave background for an integrable Hirota equation, the reduction mechanism and the characteristics of the Peregrine rogue wave in the propagation of femtosecond pulses of optical fiber are…
This is the fourth article in a series where we succeed in enlarging the class of exactly solvable quantum systems. We do that by working in a complete set of square integrable basis that carries a tridiagonal matrix representation for the…
There are well-known constructions of integrable systems which are chains of infinitely many copies of the equations of the KP hierarchy ``glued'' together with some additional variables, e.g., the modified KP hierarchy. Another…
In this paper we propose an extended Kundu-Eckhaus equation (KEE) for modeling the dynamics of skewed rogue waves emerging in the vicinity of a wave blocking point due to opposing current. The equation we propose is a KEE with an additional…
Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1)-dimensional inhomogeneous nonlinear Schrodinger (NLS) equation with variable coefficients and parabolic potential to the…
Here we consider the problem of small oscillations of a rotating inviscid incompressible fluid. From a mathematical point of view, new exact solutions to the two-dimensional Poincar\'e-Sobolev equation in a class of domains including…
The remarkable robustness of isolated columnar vortices suggests the existence of fundamental constraints that prevent spontaneous disintegration. In this work, we investigate the weakly nonlinear stability of such flows, demonstrating that…
We consider a fifth-order Kadomtsev-Petviashvili equation which arises as a two-dimensional model in the classical water-wave problem. This equation possesses a family of generalized line solitary waves which decay exponentially to periodic…
In this paper, we derive a Darboux transformation of the Hirota and the Maxwell-Bloch(H-MB) system which is governed by femtosecond pulse propagation through an erbium doped fibre and further generalize it to the matrix form of the $n$-fold…
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.…
We derive the rogue wave solution of the classical massive Thirring model, that describes nonlinear optical pulse propagation in Bragg gratings. Combining electromagnetically induced transparency with Bragg scattering four-wave mixing, may…
In this work, we focus on the construction of Nth-rouge wave solutions for the Hirota equation by utilizing the bilinear method. The formula can be represented in terms of determinants. In addition, some interesting dynamic patterns of…
The height of an $n$th-order fundamental rogue wave $q_{\rm rw}^{[n]}$ for the nonlinear Schr\"odinger equation, namely $(2n+1)c$, is proved directly by a series of row operations on matrices appeared in the $n$-fold Darboux transformation.…
The derivative nonlinear Schrodinger (DNLS) equation is the canonical model for dynamics of nonlinear waves in plasma physics and optics. We study exact solutions describing rogue waves on the background of periodic standing waves in the…
The second order perturbative field equations for slowly and rigidly rotating perfect fluid balls of Petrov type D are solved numerically. It is found that all the slowly and rigidly rotating perfect fluid balls up to second order,…
Oceanic internal waves often have curvilinear fronts and propagate over various currents. We present the first study of long weakly-nonlinear internal ring waves in a three-layer fluid in the presence of a background linear shear current.…
Rogue waves named by oceanographers are ubiquitous in nature and appear in a variety of different contexts such as water waves, liquid Helium, nonlinear optics, microwave cavities, etc. In this letter, we propose a novel type of exact…
Lump solutions are spatially rationally localized solutions which usually arise as solutions to higher dimensional nonlinear partial differential equations often possessing Hirota bilinear forms. Under some parameter constraint, these…
We study rational solutions of the Boussinesq equation, which is a soliton equation solvable by the inverse scattering method. These rational solutions, which are algebraically decaying and depend on two arbitrary parameters, are expressed…
A new exactly solvable (1+1)-dimensional complex nonlinear wave equation exhibiting rich ana- lytic properties has been introduced. A rogue wave (RW), localized in space-time like Peregrine RW solution, though richer due to the presence of…