In this paper, in order to extend the lattice Boltzmann method to deal with more nonlinear equations, a onedimensional (1D) lattice Boltzmann scheme with an amending function for the nonlinear Klein-Gordon equation is proposed. With the Taylor and Chapman-Enskog expansion, the nonlinear Klein-Gordon equation is recovered correctly from the lattice Boltzmann equation. The method is applied on so...

In this paper, we find the exact solutions of some nonlinear evolution equations by using ( ′ G )expansion method. Four nonlinear models of physical significance i.e. the symmetric regularized longwave equation, the Klein-Gordon-Zakharov equations, the Burgers-Kadomtsev-Petviashvili equation and the nonlinear Schrödinger equation with a cubic nonlinearity are considered and obtained their exact...

The general, linear equations with constant coefficients on quantum Minkowski spaces are considered and the explicit formulae for their conserved currents are given. The proposed procedure can be simplified for ∗-invariant equations. The derived method is then applied to Klein-Gordon, Dirac and wave equations on different classes of Minkowski spaces. In the examples also symmetry operators for ...

In this paper, we restudy the Green function expressions of field equations. We derive the explicit form of the Green functions for the Klein-Gordon equation and Dirac equation, and then estimate the decay rate of the solution to the linear equations. The main motivation of this paper is to show that: (1). The formal solutions of field equations expressed by Green function can be elevated as a ...

Generalizations of the three main equations of quantum physics, namely, the Schrödinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear terms, characterized by exponents depending on an index q, are considered in such a way that the standard linear equations are recovered in the limit q→1. Interestingly, these equations present a common, solitonlike, traveling solution, which is wri...

We study the 2D coupled wave–Klein-Gordon systems with semilinear null nonlinearities Q0 and Qαβ. The main result states that solution to system exists globally provided initial data is small in some weighted Sobolev space, which does not necessarily have compact support, we also asymptotic behavior of solution. In particular, show optimal time decay scattering major difficulties lie slow natur...

Consider the Klein–Gordon–Zakharov equations in $${\mathbb {R}}^{1+2}$$ , and we are interested establishing small global solution to investigating pointwise asymptotic behavior of solution. The can be regarded as a coupled semilinear wave Klein–Gordon system with quadratic nonlinearities which do not satisfy null conditions, fact that components decay sufficiently fast makes it harder conduct ...

In a previous work of ours, the most general family Kerr deformations -- admitting Carter constant has been presented. This time simple, necessary and sufficient condition in order for aforementioned to have separable Klein-Gordon equations is exhibited.

We study some systems of non-linear PDE's (Eqs. 1.1 below) which can be regarded either as generalizations of the sine-Gordon equation or as two-dimensional versions of the Toda lattice equations. We show that these systems have an infinite number of non-trivial conservation laws and an infinite number of symmetries. The second result is deduced from the first by a variant of the Hamiltonian fo...