Related papers: The Gross-Pitaevskii equation: B\"acklund transfor…
We propose a method to identify and classify evolution equations and systems that can be multipotentialised in given target equations or target systems. We refer to this as the {\it converse problem}. Although we mainly study a method for…
Linear and nonlinear Hodge-like systems for 1-forms are studied, with an assumption equivalent to complete integrability substituted for the requirement of closure under exterior differentiation. The systems are placed in a variational…
We consider five-point differential-difference equations. Our aim is to find integrable modifications of the Ito-Narita-Bogoyavlensky equation related to it by non-invertible discrete transformations. We enumerate all modifications…
We consider the (coupled) Davey-Stewartson (DS) system and its B\"{a}cklund transformations (BT). Relations among the DS system, the double Kadomtsev-Petviashvili (KP) system and the Ablowitz-Ladik hierarchy (ALH) are established. The DS…
We use the middle convolution to obtain some old and new algebraic solutions of the Painlev\'e VI equations.
Integrable equations exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants. The most basic and important example is the KdV equation and the corresponding Schwarz-KdV equation. Other…
We provide a method which takes an auto-B\"acklund transformation (auto-BT) and produces another auto-BT for a different equation. We apply the method to the natural auto-BTs for the ABS quad equations, which gives rise to torqued versions…
We study the existence of weak solutions of a generalized Gross-Pitaewskii equation, with time and space dependent coefficients that could blow up or vanish asymptotically in time, with initial data not necessarily segregated. We also study…
We investigate basic features of Bianchi's B\"acklund transformation of quadrics to see if it can be obtained under weaker assumptions and if it can be generalized to deformations of other surfaces.
We introduce a time-dependent projected Gross-Pitaevskii equation to describe a partially condensed homogeneous Bose gas, and find that this equation will evolve randomised initial wave functions to equilibrium. We compare our numerical…
In the paper we discuss the B\"acklund transformation of the KdV equation between solitons and solitons, between negatons and negatons, between positons and positons, between rational solution and rational solution, and between complexitons…
The stochastic Gross-Pitaevskii equation and modified Popov theory are shown to provide an ab initio description of finite temperature, weakly-interacting two-dimensional Bose gas experiments. Using modified Popov theory, a systematic…
We construct exact ring soliton-like solutions of the cylindrically symmetric (i.e., radial) Gross- Pitaevskii equation with a potential, using the similarity transformation method. Depending on the choice of the allowed free functions, the…
Using the linearized version of the time dependent Gross-Pitaevskii equation we calculate the dynamic response of a Bose-Einstein condensed gas to periodic density and particle perturbations. The zero temperature limit of the…
The Gross-Pitaevskii equation is a widely used model in physics, in particular in the context of Bose-Einstein condensates. However, it only takes into account local interactions between particles. This paper demonstrates the validity of…
We extend Painlev\'e IV model by adding quadratic terms to its Hamiltonian obtaining two classes of models (coalescence and deformation) that interpolate between Painlev\'e IV and II equations for special limits of the underlying…
It is well-known that the {\it Gross-Pitaevskii} variational formula describes the the ground state energy of of $N$-indistinguishable trapped particles (bosons) in a dilute state in the large system size $N\to\infty$. The goal of the…
By using the Lie's invariance infinitesimal criterion we obtain the continuous equivalence transformations of a class of nonlinear Schr\"{o}dinger equations with variable coefficients. Starting from the equivalence generators we construct…
This contribution is dedicated to the exploration of exponential operator splitting methods for the time integration of evolution equations. It entails the review of previous achievements as well as the depiction of novel results. The…
Painlev\'{e} test of the coupled Gross-Pitaevskii equations has been carried out with the result that the coupled equations pass the P-test only if a special relation containing system parameters (masses, scattering lengths) is satisfied.…