Related papers: Rational Solutions to the ABS List: Transformation…
For Light-cone gauge of Green-Schwarz superstring in AdS_5 x S^5 background, we fix two bosonic variables x^{+}=\tau and y^{9}=\sigma, and then perform the partial Legendre transformation of the remaining bosonic variables. We then obtain a…
We consider quasilinear, multi-variable, constant coefficient, lattice equations defined on the edges of the elementary square of the lattice, modeled after the lattice modified Boussinesq (lmBSQ) equation, e.g., $\tilde y z=\tilde x-x$.…
In this article, our main concern is to study the existence of bound and ground state solutions for the following fractional system of nonlinear Schr\"odinger-Korteweg-De Vries (NLS-KdV, in short) equations with Hardy potentials:…
This paper describes an extension of Fourier approximation methods for multivariate functions defined on the torus $\mathbb{T}^d$ to functions in a weighted Hilbert space $L_{2}(\mathbb{R}^d, \omega)$ via a multivariate change of variables…
Classical string actions in AdS(3) and dS(3) can be connected to the sinh-Gordon and cosh-Gordon equations through Pohlmeyer reduction. We show that the problem of constructing a classical string solution with a given static or…
Under the Flaschka-Newell Lax pair, the Darboux transformation for the Painlev\'{e}-II equation is constructed by the limiting technique. With the aid of the Darboux transformation, the rational solutions are represented by the Gram…
In this paper, we are concerned with normalized solutions in $H_{r}^{1}(\mathbb{R}^{3}) \times H_{r}^{1}(\mathbb{R}^{3})$ for Hartree-Fock type systems with the form \be\lab{ Hartree-Fock} \left\{ \begin{array}{ll} -\Delta u +\alpha \phi…
For slowly-varying initial data, solutions to the Ablowitz-Ladik system have been proven to converge to solutions of the cubic Schr\"odinger equation. In this paper we show that in the continuum limit, solutions to the Ablowitz-Ladik system…
In 2014, Chen and Singer solved the summability problem of bivariate rational functions. Later an algorithmic proof was presented by Hou and the author. In this paper, the algorithm will be simplified and adapted to the $q$-case.
In this paper, the third in a series, we continue to study the generalized Lam\'{e} equation H$(n_0,n_1,n_2,n_3;B)$ with the Darboux-Treibich-Verdier potential \begin{equation*} y^{\prime \prime }(z)=\bigg[…
A three-step method due to Nijhoff and Bobenko & Suris to derive a Lax pair for scalar partial difference equations (P\Delta Es) is reviewed. The method assumes that the P\Delta Es are defined on a quadrilateral, and consistent around the…
The paper presents the unified technique for constructing SUSY ladders of rational Liouville potentials (RLPs) starting from the so-called "Gauss-reference" (GRef) potentials exactly quantized on the line via classical Jacobi, classical…
We propose a new formulation of the Korteweg-de Vries equation (KdV) on the real line, via a gauge transform. While KdV and the gauged equation are equivalent for smooth solutions, the latter is better behaved at low regularity in…
It is shown that using the similarity transformations, a set of three-dimensional p-q nonlinear Schrodinger (NLS) equations with inhomogeneous coefficients can be reduced to one-dimensional stationary NLS equation with constant or varying…
In this paper we prove the existence of solutions to the cubic NLS equation with convolution potentials on two dimensional irrational tori undergoing an arbitrarily large growth of Sobolev norms as time evolves. Our results apply also to…
Quaternion-valued solutions to the non-commutative KdV equation are produced using determinants. The solutions produced in this way are (breather) soliton solutions, rational solutions, spatially periodic solutions and hybrids of these…
In this paper we study different Hamiltonian systems with polynomial and rational Hamiltonians associated with the generic third Painlev\'e equation and present explicit birational transformations relating them.
In this paper, we take advantage of the bilinearization reduction method to consider the local and nonlocal reduction of a discrete Ablowitz-Kaup-Newell-Segur equation. Exact solutions in double Casoratian form to the reduced nonlocal…
The duality between a class of the Davey-Stewartson type coupled systems and a class of two-dimensional Toda type lattices is discussed. A new coupled system related to the recently found lattice is presented. A method for eliminating…
We describe the screened Korringa-Kohn-Rostoker (KKR) method and the third-generation linear muffin-tin orbital (LMTO) method for solving the single-particle Schroedinger equation for a MT potential. The simple and popular formalism which…