Related papers: Linearisable systems and the Gambier approach
Lattice systems with certain Lie algebraic or quantum Lie algebraic symmetries are constructed. These symmetric models give rise to series of integrable systems. As examples the $A_n$-symmetric chain models and the SU(2)-invariant ladder…
A new method is proposed to generate nonlinear integrable systems by starting with existing Lax pair and a new form of Kr\"onecker product. It is observed that such equation can be generated with the help of a Hamiltonian structure.…
Linearization of coupled second order nonlinear ordinary differential equations (SNODEs) is one of the open and challenging problems in the theory of differential equations. In this paper we describe a simple and straightforward method to…
The convergence analysis of a third-order scheme for the highly nonlinear Landau-Lifshitz-Gilbert equation with a non-convex constraint is considered. In this paper, we first present a fully discrete semi-implicit method for solving the…
We present high order explicit geometric integrators to solve linear-quadratic optimal control problems and $N$-player differential games. These problems are described by a system coupled non-linear differential equations with boundary…
In this dissertation we study basic local differential geometry, projective differential geometry, and prolongations of overdetermined geometric partial differential equations. It is simple to prolong an n-th order linear ordinary…
The completeness of the group classification of systems of two linear second-order ordinary differential equations with constant coefficients is delineated in the paper. The new cases extend what has been done in the literature. These cases…
We deal with the construction of linear connections associated with second order ordinary differential equations with and without first order constraints. We use a novel method allowing glueing of submodule covariant derivatives to produce…
In this paper, we introduce an iterative process which converges strongly to a common element of sets of solutions of finite family of generalized equilibrium problems, sets of fixed points of finite family of continuous relatively…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
The questions of global topological, smooth and holomorphic classifications of the differential systems, defined by covering foliations, are considered. The received results are applied to nonautonomous linear differential systems and…
A linearizable version of multidimensional system of $n$-wave type nonlinear PDEs is proposed. This system is derived using the spectral representation of its solution via the procedure similar to the dressing method for the ISTM-integrable…
In this paper, the coupled fractional Ginzburg-Landau equations are first time investigated numerically. A linearized implicit finite difference scheme is proposed. The scheme involves three time levels, is unconditionally stable and…
We present several second-order linear differential equations that are associated to a particular Riccati equation with only one constant parameter in its coefficients through the technique of supersymmetric factorizations and through a…
For the system of second order quasilinear parabolic equations the problem of reducing them to the equations of diffusion type is considered. In non-degenerate case an effective algorithm for solving this problem is suggested.
We use the geometric approach to the theory of Lie systems of differential equations in order to study dissipative Ermakov systems. We prove that there is a superposition rule for solutions of such equations. This fact enables us to express…
We explore new symmetries in two-component third-order Burgers' type systems in (1+1)-dimension using Wang's O-scheme. We also find a master symmetry for a (2+1)-dimensional Davey-Stewartson type system. These results shed light on the…
We take a third-order approach to the fourth Painlev\'e equation and indicate the value of such an approach to other second-order ODEs in the Painlev\'e-Gambier list of 50.
We show that the conditions imposed on a second order linear differential equation with rational coefficients on the complex line by requiring it to have regular singularities with fixed exponents at the points of a finite set $P$ and…
We study first-order ordinary differential equations such that the intrinsic Gauss curvature of the associated surface depends only on the independent variable: $\mathcal{K}(x,u)=\kappa(x)$, showing that this geometrically motivated class…