First integrals of difference equations that do not have a variational formulation

Superintegrable systems with spin induced by co-algebra symmetry

Classical and quantum superintegrability with applications

Continuous symmetries of Lagrangians and exact solutions of discrete equations

Infinite families of superintegrable systems separable in subgroup coordinates

Superintegrable systems with spin et second-order integrals of motion

Third-order superintegrable systems separable in parabolic coordinates

Solvable Lie algebras with Borel nilradicals

Contact transformations for difference schemes

Symmetries of the continuous and discrete Krichever-Novikov equation

Are there contact transformations for discrete equations?

A nonseparable quantum superintegrable system in 2D real Euclidean space

Lie point symmetries of differential-difference equations

Third-order superintegrable systems separating in polar coordinates

An infinite family of superintegrable deformations of the Coulomb potential

Periodic orbits for an infinite family of classical superintegrable systems

Invariant difference schemes and their application to ${\rm sl}(2,\Bbb R)$ invariant ordinary differential equations

Integrable and superintegrable systems with spin in three-dimensional Euclidean space

An infinite family of solvable and integrable quantum systems on a plane

All solvable extensions of a class of nilpotent Lie algebras of dimension $n$ and degree of nilpotency $n-1$

Reduction of superintegrable systems: the anisotropic harmonic oscillator

Symmetry preserving discretization of ${\rm SL}(2,\Bbb R)$ invariant equations

Superintegrable systems with third-order integrals of motion

Heisenberg algebra, umbral calculus and orthogonal polynomials

Erratum: ``Polynomial Poisson algebras for classical superintegrable systems with a third order integral of motion'' [J. Math. Phys. {\bf 48} (2007), no. 1, 012902, 16 pp.; MR2292612]

Erratum: ``A class of superintegrable systems of Calogero type'' [J. Math. Phys. {\bf 47} (2006), no. 9, 093505, 8 pp.; èfcno 2263659]

Polynomial Poisson algebras for classical superintegrable systems with a third-order integral of motion

Quasiseparation of variables in the Schrödinger equation with a magnetic field

Integrable and superintegrable systems with spin

A class of superintegrable systems of Calogero type

Difference schemes with point symmetries and their numerical tests

Continuous symmetries of difference equations

Discretization of partial differential equations preserving their physical symmetries

Subgroup type coordinates and the separation of variables in Hamilton-Jacobi and Schrödinger equations

A class of solvable Lie algebras and their Casimir invariants

Umbral calculus, difference equations and the discrete Schrödinger equation

Lie symmetries and exact solutions of first-order difference schemes

Equivalence classes and symmetries of the variable coefficient Kadomtsev-Petviashvili equation

Discrete matrix Riccati equations with superposition formulas

Integrable and superintegrable quantum systems in a magnetic field

Continuous symmetries of Lagrangians and exact solutions of discrete equations

Symmetries, Lagrangian formalism and integration of second order ordinary difference equations

Superintegrable systems in Darboux spaces

Weak transversality and partially invariant solutions

Lie symmetries and superintegrability in quantum mechanics

A superintegrable time-dependent system with Kac-Moody symmetry

Generalized Kadomtsev-Petviashvili equation with an infinite-dimensional symmetry algebra

Superintegrability with third-order integrals in quantum and classical mechanics

Lie point symmetries and commuting flows for equations on lattices

Separation of variables and subgroup bases on $n$-dimensional hyperboloids

Quantum superintegrability and exact solvability in $n$ dimensions

Superintegrability in a two-dimensional space of nonconstant curvature

Derivation of Graf's addition theorem by contractions of the group $\rm SO(3)$

Lie symmetries of multidimensional difference equations

Invariants of the nilpotent and solvable triangular Lie algebras

Symmetries of the discrete nonlinear Schrödinger equation

Group foliation and non-invariant solutions of the heavenly equation

Symmetry classification of diatomic molecular chains

Exact solvability of superintegrable systems

Recursion operators, higher-order symmetries and superintegrability in quantum mechanics

Continuous symmetries of equations on lattices

Relation between Bäcklund transformations and higher continuous symmetries of the Toda equation

Time-dependent realization of the infinite-dimensional hydrogen algebra

Contractions of Lie algebras and the separation of variables: interbase expansions

Superintegrable systems in quantum mechanics and classical Lie theory

Lie point symmetries of difference equations and lattices

Invariant solutions of hydrodynamic-type equations

Point symmetries of generalized Toda field theories. II. Symmetry reduction

Bases for representations of quantum algebras

Lie point symmetry preserving discretizations for variable coefficient Korteweg-de Vries equations

Lie algebra contractions and symmetries of the Toda hierarchy

Discrete systems related to some equations of the Painlevé-Gambier classification

Huygens' principle and separation of variables

Integrable and superintegrable Hamiltonian systems in magnetic fields

Point symmetries of generalized Toda field theories

Lie group classification of second-order ordinary difference equations

Solutions of nonlinear differential and difference equations with superposition formulas

Singularity analysis, balance equations and soliton solution of the nonlocal complex Ginzburg-Landau equation

Nonlinear superposition formulas based on imprimitive group action

Symmetries of discrete dynamical systems involving two species

Symmetries of the discrete Burgers equation

Maximal abelian subalgebras of $e(p,q)$ algebras

Group invariant solutions for the $N=2$ super Korteweg-de-Vries equation

Contractions of Lie algebras and separation of variables. The $n$-dimensional sphere

Graded contractions of the Lie algebra $e(2,1)$

Lie group contractions and separation of variables

Discretizing families of linearizable equations

Solvable Lie algebras with triangular nilradicals

Solutions of $(2+1)$-dimensional spin systems

Maximal abelian subgroups of the isometry and conformal groups of Euclidean and Minkowski spaces

$P_\infty$ algebra of KP, free fermions and $2$-cocycle in the Lie algebra of pseudodifferential operators

$P_\infty$-algebra of symmetries of the Kadomtsev-Petviashvili equations, free fermions and $2$-cocycles in the Lie algebra of pseudodifferential operators

Lie-theoretical generalization and discretization of the Pinney equation

Symmetries and solutions of the vector nonlinear Schrödinger equation

Algebra of pseudodifferential operators and symmetries of equations in the Kadomtsev-Petviashvili hierarchy

Successive refinements of gradings and graded contractions of ${\rm sl}(3,{\bf C})$

Contractions of Lie algebras and separation of variables. Two-dimensional hyperboloid

Lie group formalism for difference equations

Grading refinements in the contractions of Lie algebras and their invariants

Contractions of Lie algebras and separation of variables

Symmetries of discrete dynamical systems

The conformal group ${\rm SU}(2,2)$ and integrable systems on a Lorentzian hyperboloid

Superposition formulas for pseudounitary matrix Riccati equations

On the solutions of the ${\bf C}{\rm P}^1$ model in $(2+1)$ dimensions

Classical and quantum integrable systems in $\widetilde{\germ g\germ l}(2)^{+*}$ and separation of variables

Harmonics on hyperspheres, separation of variables and the Bethe ansatz

Maximal abelian subalgebras of complex Euclidean Lie algebras

Generalized Casimir operators of solvable Lie algebras with abelian nilradicals

Solvable Lie algebras with abelian nilradicals

Symmetries and conditional symmetries of a nonrelativistic Chern-Simons system

Symmetry analysis of the Infeld-Rowlands equation

Symmetry classes of variable coefficient nonlinear Schrödinger equations

Representations of the quantum algebra ${\rm su}_q(2)$ on a real two-dimensional sphere

On the relation between weak and strong invariance of differential equations

Integrable systems based on ${\rm SU}(p,q)$ homogeneous manifolds

Symmetries and conditional symmetries of differential-difference equations

On the symmetry groups of the intrinsic generalized wave and sine-Gordon equations

Group theory and solutions of classical field theories with polynomial nonlinearities

Solvable Lie algebras with Heisenberg ideals

Evolution equations invariant under two-dimensional space-time Schrödinger group

Symmetries of variable coefficient Korteweg-de-Vries equations

Partially invariant solutions of a class of nonlinear Schrödinger equations

Allowed transformations and symmetry classes of variable coefficient Korteweg-de-Vries equations

Partially invariant solutions of nonlinear Klein-Gordon and Laplace equations

Maximal abelian subalgebras of pseudo-orthogonal Lie algebras

Exact solutions of the stimulated-Raman-scattering equations

Symmetry properties and solutions of nonlinear dispersive thin-film equations in three dimensions

The computer calculation of Lie point symmetries of large systems of differential equations

Graded contractions of ${\rm sl}(3,{\bf C})$

Nonclassical symmetry reductions for the Kadomtsev-Petviashvili equation

Continuous symmetries of discrete equations

Group theoretical analysis of dispersive long wave equations in two space dimensions

Maximal abelian subalgebras of complex orthogonal Lie algebras

Periodicity and quasi-periodicity for super-integrable Hamiltonian systems

Superposition formulas for nonlinear superequations

Point symmetries of conditionally integrable nonlinear evolution equations

Maximal abelian subalgebras of pseudounitary Lie algebras

Nonlinear equations invariant under the Poincaré, similitude, and conformal groups in two-dimensional space-time

Symmetries of semiclassical gravity in two dimensions

Analysis and applications of the symmetry group of the multidimensional three-wave resonant interaction problem

Group theoretical analysis of a rotating shallow liquid in a rigid container

Nonclassical symmetry reduction: example of the Boussinesq equation

Solitons in shallow seas of variable depth and in marine straits

Symmetries of the self-dual Einstein equations. I. The infinite-dimensional symmetry group and its low-dimensional subgroups

Lie symmetries of a generalised nonlinear Schrödinger equation. III. Reductions to third-order ordinary differential equations

Lie symmetries of a generalised nonlinear Schrödinger equation. II. Exact solutions

Exact solutions of the cubic and quintic nonlinear Schrödinger equation for a cylindrical geometry

Exact solutions of the spherical quintic nonlinear Schrödinger equation

Nonlinear equations with superposition formulas and exceptional group $G_2$. III. The superposition formulas

On the identification of a Lie algebra given by its structure constants. I. Direct decompositions, Levi decompositions, and nilradicals

Lie algebras under constraints and nonbijective canonical transformations

Lie symmetries of a generalised nonlinear Schrödinger equation. I. The symmetry group and its subgroups

The cylindrical Kadomtsev-Petviashvili equation: its Kac-Moody-Virasoro algebra and relation to KP equation

Equations invariant under the symmetry group of the Kadomtsev-Petviashvili equation

The classification of complete sets of operators commuting with the Dirac operator in Minkowski space-time

On the infinite-dimensional symmetry group of the Davey-Stewartson equations

Integrable nonlinear equations for water waves in straits of varying depth and width

Dynamical invariance algebra of the Hartmann potential

PASCAL programs for the identification of Lie algebras. II. SPLIT---a program to decompose parameter-free and parameter-dependent Lie algebras into direct sums

Exact solutions of the multidimensional classical $\phi^6$-field equations obtained by symmetry reduction

Nonlinear differential equations and Lie superalgebras

Superposition formulas for the rectangular matrix Riccati equations

Nonlinear equations with superposition formulas and the exceptional group $G_2$. II. Classification of the equations

New classes of exact solutions of the $\phi^6$ model in $3+1$ dimensions

ODEPAINLEVE---a MACSYMA package for Painlevé analysis of ordinary differential equations

Bäcklund transformations and the infinite-dimensional symmetry group of the Kadomtsev-Petviashvili equation

Are all the equations of the Kadomtsev-Petviashvili hierarchy integrable?

Nonlinear equations with superposition formulas and the exceptional group $G_2$. I. Complex and real forms of $g_2$ and their maximal subalgebras

On the integrability and perturbations of systems of ODEs with nonlinear superposition principles

Symmetry reduction for the Kadomtsev-Petviashvili equation using a loop algebra

On the integrability of systems of nonlinear ordinary differential equations with superposition principles

Complex parabolic subgroups of $G_2$ and nonlinear differential equations

Simple subgroups of simple Lie groups and nonlinear differential equations with superposition principles

Integrable Hamiltonian systems with velocity-dependent potentials

Subalgebras of loop algebras and symmetries of the Kadomtsev-Petviashvili equation

Abelian integrals and the reduction method for an integrable Hamiltonian system

Superposition laws for solutions of differential matrix Riccati equations arising in control theory

Separation of variables for the Hamilton-Jacobi equation on complex projective spaces

Nonlinear superposition principles: a new numerical method for solving matrix Riccati equations

Classification of systems of nonlinear ordinary differential equations with superposition principles

Comments on superposition rules for nonlinear coupled first-order differential equations

Symmetry reduction for nonlinear relativistically invariant equations

Nonlinear equations with superposition principles and the theory of transitive primitive Lie algebras

Maximal abelian subalgebras of real and complex symplectic Lie algebras

Completely integrable relativistic Hamiltonian systems and separation of variables in Hermitian hyperbolic spaces

Normal forms of elements of classical real and complex Lie and Jordan algebras

Superposition principles for matrix Riccati equations

Solutions of the multidimensional sine-Gordon equation obtained by symmetry reduction

Pseudopotentials and Lie symmetries for the generalized nonlinear Schrödinger equation

Systems of ordinary differential equations with nonlinear superposition principles

Group theoretical approach to superposition rules for systems of Riccati equations

Subgroups of Lie groups and separation of variables

On the maximal abelian subgroups of the linear classical algebraic groups

On the maximal abelian subgroups of the quadratic classical algebraic groups

Discrete two-variable expansions of scattering amplitudes for particles with spin

Quadratic Hamiltonians in phase space and their eigenstates

Polynomial irreducible tensors for point groups

Sous-algèbres de Lie de l'algèbre de Schrödinger

Tensor fields invariant under subgroups of the conformal group of space-time

The optical group and its subgroups

Continuous subgroups of the fundamental groups of physics. III. The de Sitter groups

Subalgebras of real three- and four-dimensional Lie algebras

Symmetry breaking interactions for the time dependent Schrödinger equation

On bases for irreducible representations of $O(3)$ suitable for systems with an arbitrary finite symmetry group

The group ${\rm O}(4)$, separation of variables and the hydrogen atom

Subgroups of the Poincaré group and their invariants

Quantum numbers for particles in de Sitter space

Subgroups of the similitude group of three-dimensional Minkowski space

Invariants of real low dimension Lie algebras

Canonical transformation and accidental degeneracy. III. A unified approach to the problem

Everything you always wanted to know about $SU(3)\supset {\rm O}(3)$

Continuous subgroups of the fundamental groups of physics. II. The similitude group

Continuous subgroups of the fundamental groups of physics. I. General method and the Poincaré group

Nagel-Moshinsky operators for discrete unitary representations of ${\rm U}(p, q)$

Complete sets of commuting operators and $O(3)$ scalars in the enveloping algebra of $S{\rm U}(3)$

The maximal solvable subgroups of ${\rm SO}(p,\,q)$ groups

The maximal solvable subgroups of the ${\rm SU}(p,\,q)$ groups and all subgroups of ${\rm SU}(2,\,1)$

Potential scattering and Galilei-invariant expansions of scattering amplitudes

Two-variable Galilei-group expansions of nonrelativistic scattering amplitudes

Invariant trilinear couplings involving both ${\rm SU}(2)$ and ${\rm SU}(1,\,1)$ states

One-parameter subgroups of unitary groups with indefinite metric and in particular of the conformal group

Crossing symmetric expansions of physical scattering amplitudes: the ${\rm O}(2,\,1)$ group and Lamé functions

Recursion and symmetry relations for the Clebsch-Gordan coefficients of the homogeneous Lorentz group

Clebsch-Gordan coefficients for the coupling of ${\rm SL}(2,\,C)$ principal-series representations

Representations of the Lorentz group: New integral relations between Legendre functions

Two-dimensional expansions of relativistic amplitudes in the Mandelstam triangle and crossing symmetric reactions

Symmetry groups in classical and quantum mechanics

On relativistic angular momentum theory

Invariant expansions of relativistic amplitudes and subgroups of the proper Lorentz group

On higher symmetries in quantum mechanics

The optical theorem for scattering of particles with arbitrary spins