Related papers: Variable Coefficient Third Order KdV Type of Equat…
We prove that all nontrivial finite subgroups of derived automorphisms of K3 surfaces of Picard number one have order two and give formulas for the numbers of their conjugacy classes. We also obtain a similar result for the subgroups which…
A new approach to double-sub equation method is introduced to construct novel solutions for the nonlinear partial differential equations. It is applied to the Korteweg-de Vries (KdV) equation and yields new complexiton solutions of both the…
In this paper we provide a complete classification of non-symplectic automorphisms of order nine of complex K3 surfaces.
The discrete KdV (dKdV) equation, the pinnacle of discrete integrability, is often thought to possess the singularity confinement property because it confines on an elementary quadrilateral. Here we investigate the singularity structure of…
Spectral problem for a self-adjoint third-order differential operator with non-local potential on a finite interval is studied. Elementary functions that are analogues of sines and cosines for such operators are described. Direct and…
The Medvedev degree of a subshift is a dynamical invariant of computable origin that can be used to compare the complexity of subshifts that contain only uncomputable configurations. We develop theory to describe how these degrees can be…
We determine the group of reductive cohomological degree $3$ invariants of all split semisimple groups of types $B$, $C$, and $D$. We also present a complete description of the cohomological invariants. As an application, we show that the…
New classes of exact solutions of the three-dimensional unsteady Navier-Stokes equations containing arbitrary functions and parameters are described. Various periodic and other solutions, which are expressed through elementary functions are…
Let $Y$ be a cubic threefold with a non-Eckardt type involution $\tau$. Our first main result is that the $\tau$-equivariant category of the Kuznetsov component $\mathcal{K}u_{\mathbb{Z}_2}(Y)$ determines the isomorphism class of $Y$ for…
In this paper we study the existence of at least one non-inner automorphism of order p of a non-abelian finite p-group of coclass 3, where p is a prime integer such that p is different from 3.
A class of multi-component integrable systems associated to Novikov algebras, which interpolate between KdV and Camassa-Holm type equations, is obtained. The construction is based on the classification of low-dimensional Novikov algebras by…
We introduce the notion of induced automorphisms in order to state a criterion to determine whether a given automorphism on a manifold of $K3^{[n]}$ type is, in fact, induced by an automorphism of a $K3$ surface and the manifold is a moduli…
Hirota's discrete KdV equation is an integrable partial difference equation on $\mathbb{Z}^2$, which approaches the Korteweg-de Vries (KdV) equation in a continuum limit. In this paper, we show that its multiplicative-discrete versions have…
In this article we classify vessels producing solutions of some completely integrable PDEs, presenting a \textit{unified} approach for them. The classification includes such important examples as Korteweg-de Vries (KdV) and evolutionary Non…
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…
The paper deals with second order abstract linear partial differential equations (LPDE) over a partial differential field with two commuting differential operators. In terms of usual differential equations the main content can be presented…
Dark equations are defined as some kinds of integrable couplings with some fields being homogeneously and linearly coupled to others. In this paper, dark equations are extended in several aspects. Taking the Korteweg-de Vrise (KdV) equation…
We provide a geometrical interpretation for the series of transformations used by Sakovich to map the third-order nonlinear evolution equation obtained by Chou and Qu to the mKdV equation. We also discuss its bi-Hamiltonian integrability as…
We provide linearizability criteria for a class of systems of third-order ordinary differential equations (ODEs) that is cubically semi-linear in the first derivative, by differentiating a system of second-order quadratically semi-linear…
We study the Whitham equations for all the higher order KdV equations. The Whitham equations are neither strictly hyperbolic nor genuinely nonlinear. We are interested in the solution of the Whitham equations when the initial values are…