相关论文: A note on the three dimensional sine--Gordon equat…

We study the elliptic sinh-Gordon and sine-Gordon equations on the real plane and we introduce new families of solutions. We use a Backlund transformation that connects the elliptic versions of sinh-Gordon and sine-Gordon equations. As an…

The Euler equations describing two-dimensional steady flows of an inviscid fluid are studied. These equations are reduced to one equation for the stream function and then, using the Hirota function, solutions of three nonlinear elliptic…

We construct soliton solutions for non-abelian loop Toda equations associated with general linear groups. Here we consider the untwisted case only and use the rational dressing method based upon appropriate block-matrix representation…

In this letter we consider the nonlinear realizations of the classical Polyakov's algebra $W_3^{(2)}$. The coset space method and the covariant reduction procedure allow us to deduce the Boussinesq equation with interchanged space and…

In this paper, we consider the 3D Jordan--Moore--Gibson--Thompson equation arising in nonlinear acoustics. First, we prove that the solution exists globally in time provided that the lower order Sobolev norms of the initial data are…

In this work a spectral theory for 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation is developed. Spectral data for such solutions are defined (following Hitchin and Bobenko) and the space of spectral…

I show that solutions of the SU(infinity) Toda field equation generating a fixed Einstein-Weyl space are governed by a linear equation on the Einstein-Weyl space. From this, obstructions to the existence of Toda solutions generating a given…

We introduce a single patch collocation method in order to compute solutions of initial value problems of partial differential equations whose spatial domains are 3-spheres. Besides the main ideas, we discuss issues related to our…

We present the numerical solution of two-point boundary value problems for a third order linear PDE, representing a linear evolution in one space dimension. The difficulty of this problem is in the numerical imposition of the boundary…

Many numerical codes now under development to solve Einstein's equations of general relativity in 3+1 dimensional spacetimes employ the standard ADM form of the field equations. This form involves evolution equations for the raw spatial…

We prove small data global existence and scattering for quasilinear systems of Klein-Gordon equations with different speeds, in dimension three. As an application, we obtain a robust global stability result for the Euler-Maxwell equations…

Requiring an infinite number of conserved local charges or the existence of an underlying linear system does not uniquely determine the Moyal deformation of 1+1 dimensional integrable field theories. As an example, the sine-Gordon model may…

In this paper, we consider the following elliptic Toda system associated to a general simple Lie algebra with multiple singular sources \begin{equation*} \begin{cases} -\Delta…

The tetrahedron equation arises as a generalization of the famous Yang--Baxter equation to the 2+1-dimensional quantum field theory and the 3-dimensional statistical mechanics. Very little is still known about its solutions. Here a…

The Ernst equation is formulated on an arbitrary Riemann surface. Analytically, the problem reduces to finding solutions of the ordinary Ernst equation which are periodic along the symmetry axis. The family of (punctured) Riemann surfaces…

A general covariant extension of Einstein\'{}s field equations is considered with a view to Numerical Relativity applications. The basic variables are taken to be the metric tensor and an additional four-vector $Z_\mu$. Einstein's solutions…

We classify all minimal models X of dimension n, Kodaira dimension n-1 and with vanishing Chern number $c_1^{n-2}c_2(X)=0$. This solves a problem of Koll\'ar. Completing previous work of Koll\'ar and Grassi, we also show that there is a…

We treat the lattice sine-Gordon equation and two of its generalised symmetries as a compatible system. Elimination of shifts from the two symmetries of the lattice sine-Gordon equation yields an integrable NLS-type system. An…

We show that for a large class of evolutionary nonlinear and nonlocal partial differential equations, symmetry of solutions implies very restrictive properties of the solutions and symmetry axes. These restrictions are formulated in terms…

By introducing a kind of special functions namely exponent-like function, cosine-like function and sine-like function, we obtain explicitly the basic structures of solutions of initial value problem at the original point for this kind of…