Laplace operators on metric graphs give rise to Klein-Gordon and wave operators. Solutions of the Klein-Gordon equation and the wave equation are studied and finite propagation speed is established. Massive, free quantum fields are then constructed, whose commutator function is just the Klein-Gordon kernel. As a consequence of finite propagation speed Einstein causality (local commutativity) ho...

In this paper, based on sinh-cosh method and sinh-Gordon expansion method,families of solutions of (2+1)-dimensional breaking soliton equation are obtained.These solutions include Jacobi elliptic function solution, soliton solution,trigonometric function solution.

in this paper, based on sinh-cosh method and sinh-gordon expansion method,families of solutions of (2+1)-dimensional breaking soliton equation are obtained.these solutions include jacobi elliptic function solution, soliton solution,trigonometric function solution.

We find that the fundamental quadratic form of classical string propagation in 2 + 1 dimensional constant curvature spacetimes solves the Sinh-Gordon equation, the Cosh-Gordon equation or the Liouville equation. We show that in both de Sitter and anti de Sitter spacetimes (as well as in the 2 + 1 black hole anti de Sitter spacetime), all three equations must be included to cover the generic str...

We derive a zero-curvature formalism for a combined sine-Gordon (sG) and modi-ed Korteweg{de Vries (mKdV) equation which yields a local sGmKdV hierarchy. In complete analogy to other completely integrable hierarchies of soliton equations, such as the KdV, AKNS, and Toda hierarchies, the sGmKdV hierarchy is recursively constructed by means of a fundamental polynomial formalism involving a spectr...

In this paper, the modified simple equation method is used to construct exact periodic and soliton solutions of some nonlinear partial differential equations. Exact solutions of the nonlinear Schrödinger equation, the Hamiltonian amplitude equation, Klein-Gordon equation in 1+2 dimension, the coupled Klein-Gordon equation, the (2 + 1)-dimensional long-wave-short-wave resonance interaction equat...

Algebro-geometric Poisson brackets for real, finite-zone solutions of the Korteweg–de Vries (KdV) equation were studied in [1]. The transfer of this theory to the Toda lattice and the sinh-Gordon equation is more or less obvious. The complex part of the finite-zone theory for the nonlinear Schrödinger equation (NS) and the sine-Gordon equation (SG) is analogous to KdV, but conditions that solut...

In this work, we extend the existing local fractional Sumudu decomposition method to solve the nonlinear local fractional partial differential equations. Then, we apply this new algorithm to resolve the nonlinear local fractional gas dynamics equation and nonlinear local fractional Klein-Gordon equation, so we get the desired non-differentiable exact solutions. The steps to solve the examples a...

Usin the Painlev test, it is shown that the only interablc nonlinear Klein-Gordon equations ux,=f(u) with f a linear combination of exponentials are the Liouville, sine-Gordon (or sinh-Gordon) and Mikhailov equations. In particular, the double sine-Gordon equation is not interable.

The Sine-Gordon equation in (1+3) dimensions has N-traveling front ("kink", "domain wall")- solutions for all N ≥ 1. A nonlinear functional of the solution, which vanishes on a single-front, maps multi-front solutions onto sets of infinitely long, but laterally bounded, rods, which move in space. Each rod is localized in the vicinity of the intersection of two Sine-Gordon fronts. The rod system...