Related papers: Higher-order solitons in the N-wave system
We study the behavior of shallow water waves over periodically-varying bathymetry, based on the first-order hyperbolic Saint-Venant equations. Although solutions of this system are known to generally exhibit wave breaking, numerical…
The vector Riemann-Hilbert problem is analyzed when the entries of its matrix coefficient are meromorphic and almost periodic functions. Three cases for the meromorphic functions, when they have (i) a finite number of poles and zeros…
Bifurcations of solitary waves propagating along the interface between two ideal fluids are considered. The study is based on a Hamiltonian approach. It concentrates on values of the density ratio close to a critical one, where the…
We study the unique recovery of time-independent lower order terms appearing in the symmetric first order perturbation of the Riemannian wave equation by sending and measuring waves in disjoint open sets of \textit{a priori} known closed…
In this paper, we are going to solve nonlinear nonlocal reverse-time six-component six-order AKNS system. We used reverse-time reduction to reduce the coupled system to an integrable six-order NLS-type equation. Starting from the spectral…
In the present paper, we are concerned with the general localized solutions for the complex short pulse equation including soliton, breather and rogue wave solutions. With the aid of a generalized Darboux transformation, we construct the…
In this work the Lippmann-Schwinger equation is used to model seismic waves in strongly scattering acoustic media. We consider the Helmholtz equation, which is the scalar wave equation in the frequency domain with constant density and…
A 4-parameter polynomial family of equations generalizing the Camassa-Holm and Novikov equations that describe breaking waves is introduced. A classification of low-order conservation laws, peaked travelling wave solutions, and Lie…
A previous study of diatomic molecules revealed that variational second-order density matrix theory has serious problems in the dissociation limit when the N-representability is imposed at the level of the usual two-index (P, Q, G) or even…
A typical system of k difference (or differential) equations can be compressed, or folded into a difference (or ordinary differential) equation of order k. Such foldings appear in control theory as the canonical forms of the controllability…
We investigate solitons and nonlinear Bloch waves in Bose-Einstein condensates trapped in optical lattices. By introducing specially designed localized profiles of the spatial modulation of the attractive nonlinearity, we construct an…
We present exact multi-parameter families of soliton solutions for two- and three-component Manakov equations in the \emph{defocusing} regime. Existence diagrams for such solutions in the space of parameters are presented. Fundamental…
We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient…
We develop a higher-order perturbation theory for large-scale structure formation involving a free-streaming hot or warm dark matter species. We focus on the case of mixed cold dark matter and massive neutrinos, although our approach is…
A soliton ensemble is a particular kind of approximation of the solution of an initial-value problem for an integrable equation by a reflectionless potential that is well adapted to singular asymptotics like the small-dispersion limit. We…
An analytical solution to the Hill problem Hamiltonian expanded about the libration points has been obtained by means of perturbation techniques. In order to compute the higher orders of the perturbation solution that are needed to capture…
Modulation instability, rogue wave and spectral analysis are investigated for the nonlinear Schrodinger equation with the higher-order terms. The modulation instability distribution characteristics from the sixth-order to the eighth-order…
We develop the effective non-Hermitian Hamiltonian approach for open systems with Neumann boundary conditions. The approach can be used for calculating the scattering matrix and the scattering function in open resonator-waveguide systems.…
The resources required to solve the general interacting quantum N-body problem scale exponentially with N, making the solution of this problem very difficult when N is large. In a previous series of papers we develop an approach for a…
We perform a classification of third order integrable systems of evolution equations with respect to higher symmetries. Applying it, we consider polynomial systems that are 0-homogeneous under a suitable weighting of variables with main…