相关论文: Contact Equivalence Problem for Nonlinear Wave Equ…

We demonstrate the application of the efficient semi-inverse asymptotic method to resonant interaction of the nonlinear normal modes belonging to different branches of the CNT vibration spectrum. Under condition of the 1:1 resonance of the…

In this paper, we propose a method, that is based on equivariant moving frames, for development of high order accurate invariant compact finite difference schemes that preserve Lie symmetries of underlying partial differential equations. In…

We analyze a system of reacting elements harmonically coupled to nearest neighbors in the continuum limit. An analytic solution is found for traveling waves. The procedure is used to find oscillatory as well as solitary waves. A comparison…

Let $ (M, g) $ be a compact manifold or a complete non-compact manifold without boundary, $ \dim M \geqslant 4 $, and not locally conformally flat. In this article, we introduce a new local method to resolve the Yamabe problem on compact…

In this paper we present a novel numerical solution procedure for semicoercive hemivariational inequalities. As a model example we consider a unilateral semicoercive contact problem with nonmonotone friction and provide numerical results…

We use E. Cartan's method to solve the problem of equivalence of the second order ordinary differential equations with respect to the pseudogroup of point transformations.

The floating structure problem describes the interaction between surface water waves and a floating body, generally a boat or a wave energy converter. As shown by Lannes in [18] the equations for the fluid motion can be reduced to a set of…

In this paper, we present a method to identify integrable complex nonlinear oscillator systems and construct their solutions. For this purpose, we introduce two types of nonlocal transformations which relate specific classes of nonlinear…

In this paper we provide a local well posedness result for a quasilinear beam-wave system of equations on a one-dimensional spatial domain under periodic and Dirichlet boundary conditions. This kind of systems provides a refined model for…

The classical wave-particle Hamiltonian is considered in its generalized version, where two modes are assumed to interact with the co-evolving charged particles. The equilibrium statistical mechanics solution of the model is worked out…

A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…

We apply E. Cartan's method of equivalence to classify 7-dimensional, 2-nondegenerate CR manifolds $M$ up to local CR equivalence in the case that the cubic form of $M$ satisfies a certain symmetry property with respect to the Levi form of…

In this paper we introduce an abstract nonsmooth optimization problem and prove existence and uniqueness of its solution. We present a numerical scheme to approximate this solution. The theory is later applied to a sample static contact…

We present a new method for constructing solutions to nonlinear evolutionary equations describing the propagation and interaction of nonlinear waves.

This paper is devoted to the extension of the recently proposed conditional symmetry method to first order nonhomogeneous quasilinear systems which are equivalent to homogeneous systems through a locally invertible point transformation. We…

We introduce an alternative to the method of matched asymptotic expansions. In the "traditional" implementation, approximate solutions, valid in different (but overlapping) regions are matched by using "intermediate" variables. Here we…

We consider some nonlinear elliptic equations on ${\mathbb R}^n$ and ${\mathbb S}^n$. By the method of moving spheres, we obtain the symmetry properties of solutions and some nonexistence results. Moreover, by the global bifurcation theory,…

It is well recognized that in auxiliary equation methods, the exact solutions of different types of auxiliary equations may produce new types of exact travelling wave solutions to nonlinear partial differential equations in hand. In this…

In the paper, the contact - boundary value problem with non-classical conditions not requiring agreement conditions is considered for a pseudoparabolic equation. The equivalence of these conditions is substantiated in the case if the…

In this work we present an extension of the Virtual Element Method with curved edges for the numerical approximation of the second order wave equation in a bidimensional setting. Curved elements are used to describe the domain boundary, as…