Related papers: The noncommutative KP hierarchy and its solution v…
We introduce and solve the non-commutative version of the Hermite-Pad\'{e} type I approximation problem. Its solution, expressed by quasideterminants, leads in a natural way to a subclass of solutions of the non-commutative Hirota (discrete…
We review the integrable systems which arise as symmetry reductions of Plebanski's heavenly equations, and their generalisations. We also show that all four-dimensional null Kahler-Einstein (or type N hyper-heavenly) metrics with symmetry…
In this paper we study the $5$th Order Kadomstev-Petviashvili (KP) equations posed on the real line. In particular we adapt the energy estimate argument from Guo-Molinet (arXiv:2404.12364v1 [math.AP]) to conclude unconditional uniqueness of…
Nonlinear systems of partial differential equations (PDEs) may permit several distinct solutions. The typical current approach to finding distinct solutions is to start Newton's method with many different initial guesses, hoping to find…
Two different Perfectly Matched Layer (PML) formulations with efficient pseudo-spectral numerical schemes are derived for the standard and non-relativistic nonlinear Klein-Gordon equations (NKGE). A pseudo-spectral explicit exponential…
We enlarge the spectral problem of a generalized D-Kaup-Newell (D-KN) spectral problem. Solving the enlarged zero-curvature equations, we produce integrable couplings. A reduction of the spectral matrix leads to a second integrable coupling…
We revisited solution of a linearized form of leading order Balitsky-Kovchegov equation (linear in S-matrix for dipole-nucleus scattering). Here we adopted dipole transverse width dependent cutoff in order to regulate the dipole integral.…
We start with a Riemann-Hilbert problem (RHP) related to a BD.I-type symmetric spaces $SO(2r+1)/S(O(2r-2s +1)\otimes O(2s))$, $s\geq 1$. We consider two Riemann-Hilbert problems: the first formulated on the real axis $\mathbb{R}$ in the…
This work consist of two interrelated parts. First, we derive massive gauge-invariant generalizations of geometric actions on coadjoint orbits of arbitrary (infinite-dimensional) groups $G$ with central extensions, with gauge group $H$…
The recently proposed supersymmetric extensions of reduced Kadomtsev-Petviashvili (KP) integrable hierarchies in $N =1,2$ superspace are shown to contain in the purely bosonic limit new types of ordinary non-supersymmetric integrable…
There are well-known constructions of integrable systems which are chains of infinitely many copies of the equations of the KP hierarchy ``glued'' together with some additional variables, e.g., the modified KP hierarchy. Another…
The relation between the $\widehat\gl(\infty)$ symmetry of the Kadomtsev-Petviashvili hierarchy and the Kac-Moody-Virasoro Lie point symmetries of the individual equations is established. The Lie point symmetries are shown to be the only…
The Balitsky-Fadin-Kuraev-Lipatov equation in the next-to-leading logarithmic approximation is solved using an iterative method. We derive the solution for forward scattering with all conformal spins. A discussion of the infrared finiteness…
The soliton solutions of two different (2+1)-dimensional equations with the third order and second order spatial spectral problems are studied by the $\bar{{\partial}}$-dressing method. The 3-reduced and 5-reduced equations of CKP equation…
Additional non-isospectral symmetries are formulated for the constrained Kadomtsev-Petviashvili (\cKP) integrable hierarchies. The problem of compatibility of additional symmetries with the underlying constraints is solved explicitly for…
We introduce a derivative-free computational framework for approximating solutions to nonlinear PDE-constrained inverse problems. The aim is to merge ideas from iterative regularization with ensemble Kalman methods from Bayesian inference…
In this paper, a complete Lie symmetry analysis of the damped wave equation with time-dependent coefficients is investigated. Then the invariant solutions and the exact solutions generated from the symmetries are presented. Moreover, a Lie…
In this article, a hybridizable discontinuous Galerkin (HDG) method is proposed and analyzed for the Klein-Gordon equation with local Lipschitz-type non-linearity. {\it A priori} error estimates are derived, and it is proved that…
We prove several dispersive estimates for the linear part of the Full Dispersion Kadomtsev-Petviashvili introduced by David Lannes to overcome some shortcomings of the classical Kadomtsev-Petviashvili equations. The proof of these estimates…
Based on the direct linearisation framework of the discrete Kadomtsev-Petviashvili-type equations presented in [Proc. R. Soc. A, 473 (2017) 20160915], six novel nonautonomous differential-difference equations are established, including…