Related papers: The algebraic structure behind the derivative nonl…
It is shown that nonlinear electrodynamics of the Born--Infeld theory type may be exploited to shed insight into a few fundamental problems in theoretical physics, including rendering electromagnetic asymmetry to energetically exclude…
We analytically solved the higher-order nonlinear Schrodinger (HNLS) equation with non-Kerr nonlinearity under some parametric conditions and investigated explicitly bright and dark solitary wave solutions. Periodic wave solutions are also…
The n-fold Darboux transformation (DT) is a 2\times2 matrix for the Kaup-Newell (KN) system. In this paper,each element of this matrix is expressed by a ratio of $(n+1)\times (n+1)$ determinant and $n\times n$ determinant of eigenfunctions.…
In the paper possible local and nonlocal reductions of the Ablowitz-Kaup-Newell-Suger (AKNS) hierarchy are collected, including the Korteweg-de Vries (KdV) hierarchy, modified KdV hierarchy and their nonlocal versions, nonlinear…
Two non-standard quantum deformations of the (1+1) Schr\"odinger algebra are identified with the symmetry algebras of either a space or time uniform lattice discretization of the Schr\"odinger equation. For both cases, the deformation…
The nonlinear Schr\"odinger equation (NLSE) models the slowly varying envelope dynamics of a weakly nonlinear quasi-monochromatic wave packet in dispersive media. In the context of Bose-Einstein condensate (BEC), it is often referred to as…
We obtain new coupled super Nonlinear Schrodinger equations by using AKNS scheme and soliton connection taking values in N=2 superconformal algebra.
We study Cauchy problem for the Klein-Gordon (HNLKG), wave (HNLW) and Schr\"odinger (HNLS) equations with cubic convolution (Hartree type) nonlinearity. Some global well-posedness and scattering are obtained for the (HNLKG) and (HNLS) with…
In this work, we investigate the existence and orbital (in)stability of several branches of standing--wave solutions for the cubic nonlinear Schr\"odinger equation (NLS) posed on a looping--edge graph $\mathcal{G}$, consisting of a circle…
We establish the exact solution of the nonlinear Schrodinger equation with a delta-function impurity, representing a point-like defect which reflects and transmits. We solve the problem both at the classical and the second quantized levels.…
The geometric non-linear Schrodinger equation (GNLS) on the complex Grassmannian manifold M is the Hamiltonian equation for the energy functional on C(R,M) with respect to the symplectic form induced from the Kahler form on M. It has a Lax…
The description of number of dual (quasy)-exactly solvable models with its hidden symmetry algebra has been given at different levels of analysis within the framework of generalized Kustaanheimo-Stiefel (KS)-transformations. It's shown that…
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…
We investigate the integrability of Nonlinear Partial Differential Equations (NPDEs). The concepts are developed by firstly discussing the integrability of the KdV equation. We proceed by generalizing the ideas introduced for the KdV…
A new nonlinear Schroedinger equation is obtained explicitly from the fractal Brownian motion of a massive particle with a complex-valued diffusion constant. Real-valued energy (momentum) plane wave and soliton solutions are found in the…
In our earlier papers we proposed a new approach to integrable hierarchies of soliton equations and their quantum deformations. We have applied this approach to the Toda field theories and the generalized KdV and modified KdV (mKdV)…
We show that the q-exponential function is a hypergeometric function. Accordingly, it obeys the hypergeometric differential equation. We demonstrate that this differential equation is a non-linear Schr\"odinger equation (NLSE). This NLSE…
A new approach to integrability of affine Toda field theories and closely related to them KdV hierarchies is proposed. The flows of a hierarchy are explicitly identified with infinitesimal action of the principal abelian subalgebra of the…
We study the spectral correspondence between a particular class of Schrodinger equations and supersymmetric quantum integrable model (QIM). The latter, a quantized version of the Ablowitz-Kaupp-Newell-Segur (AKNS) hierarchy of nonlinear…
We demonstrate the systematic derivation of a class of discretizations of nonlinear Schr{\"o}dinger (NLS) equations for general polynomial nonlinearity whose stationary solutions can be found from a reduced two-point algebraic condition. We…