Related papers: Complex KdV rogue waves from gauge-Miura transform…
The gravitational-wave spectrum emitted by a non-axisymmetric torus rotating at an angular velocity $\Omega_T$, is derived in terms of a structure function representing a combination of sausage-tilt modes in the torus in the limit of an…
During the past decades the study of strongly interacting fluids experienced a tremendous progress. In the relativistic heavy ion accelerators, specially the RHIC and LHC colliders, it became possible to study not only fluids made of…
We consider the (real) nonlinear wave equation $$\Box u + m^2 u + \lambda u^3 = 0, \quad m > 0, \quad \lambda > 0, $$ on four-\-dimensional Minkowski space. We introduce the complex structure and show that the (nonlinear) operator of…
The evolution of a solitary wave with very weak nonlinearity which was originally investigated by Miles [4] is revisited. The solution for a one-dimensional gravity wave in a water of uniform depth is considered. This leads to finding the…
We investigate rogue-wave solutions in a three-component coupled nonlinear Schrodinger equation. With certain requirements on the backgrounds of components, we construct a multi-rogue-wave solution that exhibits a structure like a…
In this paper, the determinant representation of the n-fold Darboux transformation (DT) of the Kundu-DNLS equation is given. Based on our analysis, the soliton solutions, positon solutions and breather solutions of the Kundu-DNLS equation…
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,…
This paper discusses the construction of a new $(3+1)$-dimensional Korteweg-de Vries (KdV) equation. By employing the KdV's recursion operator, we extract two equations, and with elemental computation steps, the obtained result is $…
We investigate the weakly nonlinear dynamics of transient gravity waves at infinite depth under the influence of a shear current varying linearly with depth. An analytical solution is permitted via integration of the Euler equations.…
A theoretical study of wave propagation in 1D metamaterial is presented. A system of nonlinear evolution equation for electromagnetic waves with both polarizations account is derived by means of projection operators method for general…
The Hirota equation is better than the nonlinear Schr\"{o}dinger equation when approximating deep ocean waves. In this paper, high-order rational solutions for the Hirota equation are constructed based on the parameterized Darboux…
General rogue wave solutions to the Sasa-Satsuma equation are constructed by the Kadomtsev-Petviashvili (KP) hierarchy reduction method. These solutions are presented in three different forms. The first form is expressed in terms of…
We verify that the fractional KdV equation is a bi-hamiltonian system using the zero curvature equation in $SL(3)$ matrix valued Lax pair representation, and explicitly find the closed form for the hamiltonian operators of the system. The…
We study the sL(3,C) mKDV string theories. We obtain the flows and the string equations. Using the generalized Miura map, we show that we have an unification of these models with the [P,Q]=Q sL(3,C) KDV ones in the framework of open-closed…
New type of localized solutions for the two-dimensional multicomponent Yajima-Oikawa system is presented. The dynamics of solutions of this type occurs on the zero background and is similar to that of rogue waves.
It is shown how the complex sine-Gordon equation arises as a symmetry flow of the AKNS hierarchy. The AKNS hierarchy is extended by the ``negative'' symmetry flows forming the Borel loop algebra. The complex sine-Gordon and the vector…
We establish precise spectral criteria for potential functions $V$ of reflectionless Schr\"odinger operators $L_V = -\partial_x^2 + V$ to admit solutions to the Korteweg de-Vries (KdV) hierarchy with $V$ as an initial value. More generally,…
Under three relations connecting the field variables of Toda flows and that of KdV flows, we present three new sequences of combination of the equations in the Toda hierarchy which have the KdV hierarchy as a continuous limit. The relation…
We consider the kinetic derivative nonlinear Schr\"odinger equation, which is a one-dimensional nonlinear Schr\"odinger equation with a cubic derivative nonlinear term containing the Hilbert transformation. In our previous work, we proved…
This article addresses the question of general rogue-wave solutions in the nonlocal parity-time-symmetric nonlinear Schrodinger equation. By generalizing the previous bilinear Kadomtsev-Petviashvili reduction method, large classes of rogue…