Related papers: Solving formally the Auxiliary System of $O(N)$ No…
We develop the Sparse Approximate Matrix Multiply ($\tt SpAMM$) $n$-body solver for first order Newton Schulz iteration of the matrix square root and inverse square root. The solver performs recursive two-sided metric queries on a modified…
A master equation expressing the classical integrability of two-dimensional non-linear sigma models is found. The geometrical properties of this equation are outlined. In particular, a closer connection between integrability and T-duality…
It is shown how a system of evolution equations can be developed both from the structure equations of a submanifold embedded in three-space as well as from a matrix SO(6) Lax pair. The two systems obtained this way correspond exactly when a…
In this paper, we investigate the integrability aspects of a physically important nonlinear oscillator which lacks sufficient number of Lie point symmetries but can be integrated by quadrature. We explore the hidden symmetry, construct a…
The Hamiltonian symmetry reduction of the geodesics system on a symmetric space of negative curvature by the maximal compact subgroup of the isometry group is investigated at an arbitrary value of the momentum map. Restricting to regular…
We construct and analyze unfolded off-shell systems for chiral and vector supermultiplets using multispinor formalism and external currents. We find that auxiliary variables of multispinor formalism allow for the interesting reorganization…
The C. Neumann system describes a particle on the sphere S^n under the influence of a potential that is a quadratic form. We study the case that the quadratic form has l+1 distinct eigenvalues with multiplicity. Each group of m_\sigma equal…
Nonlinear systems exist widely in nature, however, how to construct systems with accurate expected non-linearity artificially is still a problem, which greatly limits their experimental study and engineering application. In this paper, we…
This paper deals with the study of "\textit{sharp localized}" solutions of a nonlinear type Schr{\"o}dinger equation in the whole space $\R^N,$ $N\ge1,$ with a zero order term, in modulus, like a power $m$ less than one of the modulus of…
We establish local Calder\'on-Zygmund type estimates for weak solutions to nonlinear parabolic systems with $p$-growth and VMO coefficients. In particular, we prove that if the right-hand side belongs locally to $L^{\mu s}$, where the…
We show that the same algebraic data that permit to construct the Lax pair and the $r$-matrix of an integrable non-linear $\sigma$-model in $1+1$ dimensions can be also used for the construction of Lax pairs and of $r$-matrices of several…
In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under dissipative conditions, numerous previous works have established rigorous…
We consider the Lagrangian particle model introduced in [hep-th/9612017] for zero mass but nonvanishing second central charge of the planar Galilei group. Extended by a magnetic vortex or a Coulomb potential the model exibits conformal…
A completely integrable nonlinear partial differential equation (PDE) can be associated with a system of linear PDEs in an auxiliary function whose compatibility requires that the original PDE is satisfied. This associated system is called…
Ensuring that a PDE model is well-posed is a necessary precursor to any form of analysis, control, or numerical simulation. Although the Lumer-Phillips theorem provides necessary and sufficient conditions for well-posedness of dissipative…
We numerically examine the exterior solution of spherically symmetric and static configuration in scalar-tensor theories by using the nonminimally coupled scalar field with zero potential as our sample model. Our main purpose in this work…
A discrete analogue of the dressing method is presented and used to derive integrable nonlinear evolution equations, including two infinite families of novel continuous and discrete coupled integrable systems of equations of nonlinear…
A methodology for non-intrusive, projection-based non-linear model reduction originally presented by Renganathan et. al. (2018)~\cite{renganathan2018koopman} is further extended towards parametric systems with focus on application to…
We generalize a finite parity-time (${\cal PT}$-) symmetric network of the discrete nonlinear Schr\"odinger type and obtain general results on linear stability of the zero equilibrium, on the nonlinear dynamics of the dimer model, as well…
We pursue an analogy of the Schur-Weyl reciprocity for the spinor groups and pick up the irreducible spin representations in the tensor space $\Delta \textstyle{\bigotimes \bigotimes^k V}$. Here $\Delta$ is the fundamental representation of…