相关论文: Gardner's deformation of the Krasil'shchik-Kersten…

We solve the Gardner deformation problem for the N=2 supersymmetric a=4 Korteweg-de Vries equation (P. Mathieu, 1988). We show that a known zero-curvature representation for this superequation yields the system of new nonlocal variables…

We re-address the problem of construction of new infinite-dimensional completely integrable systems on the basis of known ones, and we reveal a working mechanism for such transitions. By splitting the problem's solution in two steps, we…

We prove that P.Mathieu's Open problem on constructing Gardner's deformation for the N=2 supersymmetric a=4-Korteweg-de Vries equation has no supersymmetry invariant solutions, whenever it is assumed that they retract to Gardner's…

Using the algebraic method of Gardner's deformations for completely integrable systems, we construct the recurrence relations for densities of the Hamiltonians for the Boussinesq and the Kaup-Boussinesq equations. By extending the Magri…

In this paper we derive a new model for visco-elasticity with large deformations where the independent variables are the stretch and the rotation tensors which intervene with second gradients terms accounting for physical properties in the…

In this thesis, I investigate how to construct a self-consistent model of deformed general relativity using canonical methods and metric variables. The specific deformation of general covariance is predicted by some studies into loop…

An algebraic definition of Gardner's deformations for completely integrable bi-Hamiltonian evolutionary systems is formulated. The proposed approach extends the class of deformable equations and yields new integrable evolutionary and…

We investigate deformations of the Kerr-(A)dS near horizon geometry and derive partial infinitesimal rigidity results for it. The proof comprises two parts. First, we follow the analysis of Jezierski and Kami\'nski [Gen Rel Grav 45 (2013)…

Nonconservative evolution problems describe irreversible processes and dissipative effects in a broad variety of phenomena. Such problems are often characterised by a conservative part, which can be modelled as a Hamiltonian term, and a…

The main object of the paper is a recently discovered family of multicomponent integrable systems of partial differential equations, whose particular cases include many well-known equations such as the Korteweg--de Vries, coupled KdV, Harry…

In this paper, we analyze a PDE system arising in the modeling of phase transition and damage phenomena in thermoviscoelastic materials. The resulting evolution equations in the unknowns \theta (absolute temperature), u (displacement), and…

We study the Cauchy problem for a system of cubic nonlinear Klein-Gordon equations in one space dimension. Under a suitable structural condition on the nonlinearity, we will show that the solution exists globally and decays of the order…

We use the integrable deformations method for a three-dimensional system of differential equations to obtain deformations of the T system. We analyze a deformation given by particular deformation functions. We point out that the obtained…

We study the 1D Klein-Gordon equation with variable coefficient nonlinearity. This problem exhibits an interesting resonant interaction between the spatial frequencies of the nonlinear coefficients and the temporal oscillations of the…

The Gardner method, traditionally used to generate conservation laws of integrable equations, is generalized to generate symmetries. The method is demonstrated for the KdV, Camassa-Holm and Sine-Gordon equations. The method involves…

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…

We use methods from exterior differential systems (EDS) to develop a geometric theory of scalar, first-order Lagrangian functionals and their associated Euler-Lagrange PDEs, subject to contact transformations. The first chapter contains an…

We generalise to the $\mathbb{Z}_2$-graded set-up a practical method for inspecting the (non)removability of parameters in zero-curvature representations for partial differential equations (PDEs) under the action of smooth families of gauge…

In this work, we introduce a degenerating PDE system with a time-depending domain for complete damage processes under time-varying Dirichlet boundary conditions. The evolution of the system is described by a doubly nonlinear differential…

A system of partial differential equations (PDEs) is derived to compute the full-field stress from an observed kinematic field when the flow rule governing the plastic deformation is unknown. These equations generalize previously proposed…