Related papers: Rogue Wave Multiplets in the Complex KdV Equation
In the present work, we explore the possibility of developing rogue waves as exact solutions of some nonlinear dispersive equations, such as the nonlinear Schr\"odinger equation, but also, in a similar vein, the Hirota, Davey-Stewartson,…
We study the existence and stability of periodic traveling-wave solutions for complex modified Korteweg-de Vries equation. We also discuss the problem of uniform continuity of the data-solution mapping.
In this paper, we study the novel nonlinear wave structures of a (2+1)-dimensional variable-coefficient Korteweg-de Vries (KdV) system by its analytic solutions. Its $N$-soliton solution are obtained via Hirota's bilinear method, and in…
We study rogue wave excitation dynamics on a double-plane wave background through deriving rogue wave solution on the background. The results indicate that rogue wave still can be excited successfully from resonant perturbations with the…
The appearance of rogue waves in deep sea is investigated using the modified nonlinear Schr\"odinger (MNLS) equation in one spatial-dimension with random initial conditions that are assumed to be normally distributed, with a spectrum…
We study stability of travelling wave solutions to Korteweg--de Vries type equations which has the fractional dispersion and integer-indices double power nonlinearities. It may depend on parity combinations of the two indices and the…
We identify a periodic reduction of the non-autonomous lattice potential Korteweg-de Vries equation with the additive discrete Painlev\'e equation with $E^{(1)}_6$ symmetry. We present a description of a set of symmetries of the reduced…
Two families of periodic traveling waves exist in the focusing mKdV (modified Korteweg-de Vries) equation. Spectral stability of these waveforms with respect to co-periodic perturbations of the same period has been previously explored by…
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…
The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\epsilon^2$, is characterized by the appearance of a zone of rapid modulated oscillations of wave-length of order $\epsilon$. These oscillations are…
This paper investigates the asymptotic behavior of high-order vector rogue wave (RW) solutions of the coupled nonlinear Schr\"odinger (CNLS) equation in the presence of multiple large internal parameters. We report several new high-order RW…
We demonstrate the control of solitary wave dynamics of modified Kortweg-de Vries (MKdV) equation through the temporal variations of the distributed coefficients. This is explicated through exact cnoidal wave and localized soliton solutions…
Generalization of the modified KdV equation to a multi-component system, that is expressed by $(\partial u_i)/(\partial t) + 6 (\sum_{j,k=0}^{M-1} C_{jk} u_j u_k) (\partial u_i)/(\partial x) + (\partial^3 u_{i})/(\partial x^3) = 0, i=0, 1,…
The relevance of perturbed forms of the Korteweg-de Vries equation to a range of physical problems is discussed. Solutions which are perturbations of solitary travelling wave solutions are then considered, focussing predominantly on the…
As an example for complex systems with extreme events we investigate ocean wave states exhibiting rogue waves. We present a statistical method of data analysis based on multi-point statistics which for the first time allows grasping extreme…
General rogue waves in (1+1)-dimensional three-wave resonant interaction systems are derived by the bilinear method. These solutions are divided into three families, which correspond to a simple root, two simple roots and a double root of a…
Rogue waves are rapid and unpredictable events of exceptional amplitude reported in various fields, such as oceanography and optics, with much of the interest being targeted towards their physical origins and likelihood of occurrence. Here,…
In the present paper, a hierarchy of the mKdV equation is integrated by the methods of algebraic geometry. The mKdV hierarchy in question arises on coadjoint orbits in the loop algebra of $\mathfrak{sl}(2)$, and employs a family of…
We present determinant expressions for vector rogue wave solutions of the Manakov system, a two-component coupled nonlinear Schr\"odinger equation. As special case, we generate a family of exact and non-symmetric rogue wave solutions of the…
This paper is dedicated to study higher-order rogue wave solutions of the coupled Hirota equations with high-order nonlinear effects like the third dispersion, self-steepening and stimulated Raman scattering terms. By using the generalized…