381 citations · 496 across the 14 of their papers we have counts for
6 papers · 1 filter
Superintegrability in the Manev Problem and its Real Form Dynamics
V. S. Gerdjikov, A. Kyuldjiev, G. Marmo +1
We report here the existence of Ermanno-Bernoulli type invariants for the Manev model dynamics which may be viewed upon as remnants of Laplace-Runge-Lenz vector whose conservation…
Selected Aspects of Soliton Theory. Constant boundary conditions
V. S. Gerdjikov
Brief review of the methods for solving the multicomponent nonlinear Schrodinger (MNLS) equations and analysis of their Hamiltonian structures is given. Main attention is paid to t…
Basic aspects of soliton theory
Vladimir S. Gerdjikov
This is a review of the main ideas of the inverse scattering method (ISM) for solving nonlinear evolution equations (NLEE), known as soliton equations. As a basic tool we use the f…
Inverse Scattering Transform for the Camassa-Holm equation
Adrian Constantin, Vladimir S. Gerdjikov, Rossen I. Ivanov
An Inverse Scattering Method is developed for the Camassa-Holm equation. As an illustration of our approach the solutions corresponding to the reflectionless potentials are explici…
On Reductions and Real Hamiltonian Forms of Affine Toda Field Theories
Vladimir S. Gerdjikov, Georgi G. Grahovski
A family of real Hamiltonian forms (RHF) for the special class of affine 1+1 - dimensional Toda field theories is constructed. Thus the method, proposed in [Mikhailov;1981] for sys…
Real Hamiltonian Forms of Affine Toda Models Related to Exceptional Lie Algebras
Vladimir S. Gerdjikov, Georgi G. Grahovski
The construction of a family of real Hamiltonian forms (RHF) for the special class of affine 1+1-dimensional Toda field theories (ATFT) is reported. Thus the method, proposed in [1…