Related papers: On Integrability of Nonautonomous Nonlinear Schroe…
A new method is proposed to generate nonlinear integrable systems by starting with existing Lax pair and a new form of Kr\"onecker product. It is observed that such equation can be generated with the help of a Hamiltonian structure.…
We propose integrable discretizations of derivative nonlinear Schroedinger (DNLS) equations such as the Kaup-Newell equation, the Chen-Lee-Liu equation and the Gerdjikov-Ivanov equation by constructing Lax pairs. The discrete DNLS systems…
We formulate an analog of Inverse Scattering Method for integrable systems on noncommutative associative algebras. In particular we define Hamilton flows, Casimir elements and noncommutative analog of the Lax matrix. The noncommutative Lax…
We determine conditions under which a generic gauge invariant nonautonomous and inhomogeneous nonlinear partial differential equation in the two-dimensional space-time continuum can be transform into standard autonomous forms. In addition…
In this paper, the inverse scattering transform for the integrable discrete nonlocal PT symmetric nonlinear Schr\"odinger equation with nonzero boundary conditions is presented. According to the two different signs of symmetry reduction and…
The present work addresses the study and characterization of the integrability of three famous nonlinear Schr\"odinger equations with derivative-type nonlinearities in 1+1 dimensions. Lax pairs for these three equations are successfully…
We study an integrable modification of the focusing nonlinear Schroedinger equation from the point of view of semiclassical asymptotics. In particular, (i) we establish several important consequences of the mixed-type limiting quasilinear…
An integrable extension of the well known nonlinear Schroedinger (NLS) equation to a higher space-dimension, recently proposed by us, is investigated, exploring its various important aspects. Focusing on the idea of construction its…
In this work we study the inverse scattering problem for the selfadjoint matrix Schrodinger operator on the half line. We provide the necessary and sufficient conditions for the solvability of the inverse scattering problem.
The Hamiltonian form of the (2+1) nonlinear integrable Schr\"odinger equation and the system of two (2+1) nonlinear analogue of the mKdV equation is proved. A well--posed Cauchy problem is formulated and the solvability of such a problem…
We develop a unified approach for construction of symplectic forms for 1D integrable equations with the periodic and rapidly decaying initial data. As an example we consider the cubic nonlinear Schr\"{o}dinger equation.
A new integrable class of Davey--Stewartson type systems of nonlinear partial differential equations (NPDEs) in 2+1 dimensions is derived from the matrix Kadomtsev--Petviashvili equation by means of an asymptotically exact nonlinear…
We propose a general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations. This allows us to give the general integrable evolution corresponding to an arbitrary time and space dependence of the…
The purpose of the present paper is to develop the inverse scattering transform for the nonlocal semi-discrete nonlinear Schrodinger equation (known as Ablowitz-Ladik equation) with PT-symmetry. This includes: the eigenfunctions (Jost…
We present a rigorous theory of the inverse scattering transform (IST) for the three-component defocusing nonlinear Schrodinger (NLS) equation with initial conditions approaching constant values with the same amplitude as $x\to\pm\infty$.…
The nonlinear Schroedinger model is a prototypical dispersive wave equation that features finite time blowup, either for supercritical exponents (for fixed dimension) or for supercritical dimensions (for fixed nonlinearity exponent). Upon…
A global solution of the Schr\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is…
The inverse scattering theory is a basic tool to solve linear differential equations and some Partial Differential Equations (PDEs). Using this theory the Korteweg-de Vries (KdV), the family of evolutionary Non Linear Schrodinger (NLS)…
We study the quantum mechanics of the derivative nonlinear Schrodinger equation which has appeared in many areas of physics and is known to be classically integrable. We find that the N-body quantum problem is exactly solvable with both…
Under investigation in this work is an extended nonlinear Schr\"{o}dinger equation with nonzero boundary conditions, which can model the propagation of waves in dispersive media. Firstly, a matrix Riemann-Hilbert problem for the equation…