Related papers: Comment on `Painlev\'e Integrability and Multi-wav…
We examine whether the Painlev\'e property is a necessary condition for the integrability of nonlinear ordinary differential equations. We show that for a large class of linearisable systems this is not the case. In the discrete domain, we…
A non-isospectral (2+1) dimensional integrable spin equation is investigated. It is shown that its geometrical and gauge equivalent counterparts is the (2+1) dimensional nonlinear Schr\"odinger equation introduced by Zakharov and studied…
We argue the integrability of the generalized KdV(GKdV) equation using the Painlev\'e test. For $d( \le 2)$ dimensional space, GKdV equation passes the Painlev\'e test but does not for $d \geq 3$ dimensional space. We also apply the…
The two-component analogue of two-dimensional long wave-short wave resonance interaction equations is derived in a physical setting. Wronskian solutions of the integrable two-component analogue of two-dimensional long wave-short wave…
The one-mode and the two-mode multiboson systems with sl(2,R) symmetry are investigated.Hamiltonians of these systems are integrated using the theory of orthogonal polynomials. The coherent state representation for these systems is…
Binary symmetry constraints of the N-wave interaction equations in 1+1 and 2+1 dimensions are proposed to reduce the N-wave interaction equations into finite-dimensional Liouville integrable systems. A new involutive and functionally…
A new technique for constructing the relativistic wave equation for the two-body system composed of the spin-1/2 and spin-0 particles is proposed. The method is based on the extension of the SL(2,C) group to the Sp(4,C) one. The obtained…
In this letter, the integrability aspects of a generalized Fisher type equation with modified diffusion in (1+1) and (2+1) dimensions are studied by carrying out a singularity structure and symmetry analysis. It is shown that the Painlev\'e…
There is a close relation between duality in $N=2$ SUSY gauge theories and integrable models. In particular, the quantum moduli space of vacua of $N=2$ SUSY $SU(3)$ gauge theories coupled to two flavors of massless quarks in the fundamental…
All Painlev\'e equations can be written as a time-dependent Hamiltonian system, and as such they admit a natural generalization to the case of several particles with an interaction of Calogero type (rational, trigonometric or elliptic).…
Upon having presented a bird's eye view of history of integrable systems, we give a brief review of certain earlier advances (arXiv:1401.2122 & arXiv:1812.02263) in the longstanding problem of search for partial differential systems in four…
Let $G=(V,E)$ be a matching-covered graph, denote by $P$ its perfect matching polytope, and by $L$ the integer lattice generated by the integral points in $P$. In this paper, we give short, polyhedral proofs for two difficult results…
Following Sutherland's work on one-dimensional integrable systems we formulate and study its two-dimensional version. Physically it expresses the absence of true 3-body forces among an assembly of N particles leaving exclusively effective…
We show that one of the five cases of a quadratic Hamiltonian, which were recently selected by Sokolov and Wolf who used the Kovalevskaya-Lyapunov test, fails to pass the Painleve test for integrability.
The quest to reveal the physical essence of the infinitely many symmetries and conservation laws that are intrinsic to integrable systems has historically posed a significant challenge at the confluence of physics and mathematics. This…
An effective way to design structured coherent wave interference patterns that builds on the theory of coherent lattices, is presented. The technique combines prime number factorization in the complex plane with moir\'e theory to provide a…
We investigate $(d+1)$-dimensional quasilinear systems which are integrable by the method of hydrodynamic reductions. In the case $d\geq 3$ we formulate a conjecture that any such system with an irreducible dispersion relation must be…
In this paper, we investigate a generalized (2+1)-dimensional Hirota-Satsuma-Ito (HSI) equation in fluid mechanics. Via the Painleve analysis, we find that the HSI equation is Painleve integrable under certain condition. Bilinear form,…
In this work we apply the Weiss, Tabor and Carnevale integrability criterion (Painlev\'e analysis) to the classical version of the two dimensional Bukhvostov-Lipatov model. We are led to the conclusion that the model is not integrable…
The need of mathematically formulate relations between composite materials' properties and its resonance response is growing. This is due the fast technological advancement in micro-material manufacturing, present in chips for instance. In…