Related papers: Deformation Conjecture: Deforming Lower Dimensiona…
We generalize earlier results of Fokas and Liu and find all locally analytic (1+1)-dimensional evolution equations of order $n$ that admit an $N$-shock type solution with $N\leq n+1$. To this end we develop a refinement of the technique…
The celebrated (1+1)-dimensional Korteweg de-Vries (KdV) equation and its (2+1)-dimensional extention, the Kadomtsev-Petviashvili (KP) equation, are two of the most important models in physical science. The KP hierarchy is explicitly…
In this paper, we continue the study of the Davey-Stewartson system which is one of the most important$(2+1)$ dimensional integrable models. As we showed in the previous paper, the dDS (dispersionless Davey-Stewartson) system arises from…
Non-autonomous degenerate KdV systems in (1+1) dimensions are considered for integrability classification. Integrability of the systems is associated with the existence of a recursion operator. Some new non-autonomous degenerate…
A set of infinitely many nonlocal conservation laws are revealed for (1+1)-dimensional evolution equations. For some special known integrable systems, say, the KdV and Dym equations, it is found that different nonlocal conservation laws can…
This work proposes an approach for latent-dynamics learning that exactly enforces physical conservation laws. The method comprises two steps. First, the method computes a low-dimensional embedding of the high-dimensional dynamical-system…
Decomposition of shapes into (approximate) convex parts is essential for applications such as part-based shape representation, shape matching, and collision detection. In this paper, we propose a novel convex decomposition using a…
A novel template matching algorithm that can incorporate the concept of deformable parts, is presented in this paper. Unlike the deformable part model (DPM) employed in object recognition, the proposed template-matching approach called…
The output of molecular dynamics simulations is high-dimensional, and the degrees of freedom among the atoms are related in intricate ways. Therefore, a variety of analysis frameworks have been introduced in order to distill complex motions…
We construct a one-parameter family of N=3 supersymmetric extensions of the KdV equation as a Hamiltonian flow on N=3 superconformal algebra and argue that it is non-integrable for any choice of the parameter. Then we propose a modified N=3…
KdV6 equation can be described as the Kupershmidt deformation of the KdV equation (see 2008, Phys. Lett. A 372: 263). In this paper, starting from the bi-Hamiltonian structure of the discrete integrable system, we propose a generalized…
Dynamic Mode Decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of non-linear systems from experimental datasets. Recently, several attempts have extended DMD to the context of low-rank approximations. This…
A typical system of k difference (or differential) equations can be compressed, or folded into a difference (or ordinary differential) equation of order k. Such foldings appear in control theory as the canonical forms of the controllability…
The fully discrete adjoint equations and the corresponding adjoint method are derived for a globally high- order accurate discretization of conservation laws on parametrized, deforming domains. The conservation law on the deforming domain…
We study the deformed Harry Dym and Hunter-Zheng equations with two arbitrary deformation parameters. These reduce to various other known models in appropriate limits. We show that both these systems are bi-Hamiltonian with the same…
We consider (3+1)-dimensional second-order evolutionary PDEs where the unknown $u$ enters only in the form of the 2nd-order partial derivatives. For such equations which possess a Lagrangian, we show that all of them have a symplectic…
We demonstrate that hydrodynamic reductions of dispersionless integrable systems in 2+1 dimensions, such as the dispersionless Kadomtsev-Petviashvili (dKP) and dispersionless Toda lattice (dTl) equations, can be deformed into reductions of…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
A method for constructing the Lax pairs for nonlinear integrable models is suggested. First we look for a nonlinear invariant manifold to the linearization of the given equation. Examples show that such invariant manifold does exist and can…
The notions of generating sets of conservation laws of systems of differential equations with respect to symmetry groups and equivalence groups are introduced and applied. This allows us to generalize essentially the procedure of finding…