Related papers: Integrable equations and classical S-matrix
Travelling waves and conservation laws are studied for a wide class of U(1)-invariant complex mKdV equations containing the two known integrable generalizations of the ordinary (real) mKdV equation. The main results on travelling waves…
The extended KdV equation is a nonlinear dispersive wave model that is asymptotically or variationally derived from the full dispersive Euler shallow water waves equations when gravity-capillary and higher order nonlinear effects are taken…
We consider unique continuation properties of solutions to a family of evolution equations. Our interest is mainly on nonlinear non-local models. This class contains the Benjamin-Ono, the Intermediate Long Wave, the Camassa-Holm, the…
We consider a generalization of the mKdV model of shallow water out-flows. This generalization is a family of equations with nonlinear dispersion terms containing, in particular, KdV, mKdV, Benjamin-Bona-Mahony, Camassa-Holm, and…
New manifestly gauge-invariant forms of two-dimensional generalized dispersive long-wave and Nizhnik-Veselov-Novikov systems of integrable nonlinear equations are presented. It is shown how in different gauges from such forms famous…
All non-equivalent integrable evolution equations of the fifth order of the form $u_t=D_x\frac{\delta H}{\delta u}$ are found.
We study the interaction of suitable small and high frequency waves evolving by the flow of the Benjamin-Ono equation. As a consequence, we prove that the flow map of the Benjamin-Ono equation can not be uniformly continuous on bounded sets…
The inverse scattering transform allows explicit construction of solutions to many physically significant nonlinear wave equations. Notably, this method can be extended to fractional nonlinear evolution equations characterized by anomalous…
We study the relevance of various scalar equations, such as inviscid Burgers', Korteweg-de Vries (KdV), extended KdV, and higher order equations (of Camassa-Holm type), as asymptotic models for the propagation of internal waves in a…
We derive amplitude equations for interface dynamics in pattern forming systems with long-range interactions. The basic condition for the applicability of the method developed here is that the bulk equations are linear and solvable by…
The relativistic five-quark equations are found in the framework of the dispersion relation technique. The behavior of the low-energy five-particle amplitude is determined by its leading singularities in the pair invariant masses. The…
This paper provides an alternative methodology for analysis of three-wave interactions under the exact dispersion relation associated with gravity waves in fluid of intermediate depth. A Korteweg-de Vries type of equation with exact…
Fifth order, quasi-linear, non-constant separant evolution equations are of the form u_t=A\frac{\partial^5 u}{\partial x^5}+\tilde{B}, where A and \tilde{B} are functions of x, t, u and of the derivatives of u with respect to x up to order…
An "exact discretization" of the Schroedinger operator is considered and its direct and inverse scattering problems are solved. It is shown that a differential-difference nonlinear evolution equation depending on two arbitrary constants can…
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…
A new type of wave-mean flow interaction is identified and studied in which a small-amplitude, linear, dispersive modulated wave propagates through an evolving, nonlinear, large-scale fluid state such as an expansion (rarefaction) wave or a…
Here, the perturbation equation for a dissipative medium is derived from the first principle from the linearized compressible Navier-Stokes equation without Stokes's hypothesis. The dispersion relations of this generic governing equation…
The propagation of ON-OFF signals with dispersive waves is examined in this study. An integral-form exact solution for a simple ON-OFF switching event is derived, which holds for any dispersion relation. The integral can be exactly…
Hawking radiation has become experimentally testable thanks to the many analogue systems which mimic the effects of the event horizon on wave propagation. These systems are typically dominated by dispersion, and give rise to a numerically…
In this paper, we present a model describing the time evolution of two dimensional surface waves in gravity and infinite depth. The model of six interacting modes derives from the normal form of the system describing the dynamics of surface…