this paper aims to study a generalized double sinh-gordon equation, which appears in several physical phenomena such as integrable quantum field theory, kink dynamics and fluid dynamics. lie symmetry analysis together with the simplest equation method is used to obtain exact solutions for this equation. moreover, we derive conservation laws for the equation by using two different approaches, na...

The dynamics of an interface between the normal and superconducting phases under nonstationary external conditions is studied within the framework of the time-dependent Ginzburg-Landau equations of superconductivity, modified to include thermal fluctuations. An equation of motion for the interface is derived in two steps. First, the method of matched asymptotic expansions is used to derive a di...

In previous report (J. Phys. A (1997) 30 4019-4029), I showed that the Dirac field confined in a surface immersed in R 3 by means of a mass type potential is governed by the Konopelchenko-Kenmotsu-Weierstrass-Enneper equation. In this article, I quantized the Dirac field and calculated the gauge transformation which exhibits the gauge freedom of the parameterization of the surface. Then using t...

The study of extremal Kähler metric is initiated by the seminal works of Calabi [4], [5]. Let (M, [ω]) be a compact Kähler manifold with fixed Kähler class [ω]. For any Kähler metrics g in the fixed Kähler class [ω], the Calabi energy C(g) is defined as C(g) = M s 2 dµ, where s is the scalar curvature of g. The extremal Kähler metric is the critical point of the Calabi energy. The Euler-Lagrang...

Keywords: Allen–Cahn equation Finite element method Operator splitting method Unconditionally stable scheme a b s t r a c t We present an unconditionally stable hybrid finite element method for solving the Allen– Cahn equation, which describes the temporal evolution of a non-conserved phase-field during the antiphase domain coarsening in a binary mixture. Its various modified forms have been ap...

In this paper, we illustrated one scenario to modify the Ivanenko-LandauKähler equation. Since Ivanenko and Landau introduced the equation in 1928, the equation has been regarded as having a certain role as a fermion in particular in the discrete Lattice. Also, although it correctly is formulated as an alternative classical field equation by the Ideal projection for the Dirac equation in the Mi...

In a 5-dimensional spacetime (M, gab) with a Killing vector field ξ a which is either everywhere timelike or everywhere spacelike, the collection of all trajectories of ξ gives a 4-dimensional space S. The reduction of (M, gab) is studied in the geometric language, which is a generalization of Geroch’s method for the reduction of 4-dimensional spacetime. A 4dimensional gravity coupled to a vect...

Soliton solutions of the perturbedLandau-Lifshitz equation, S t = [S × Sxx ] + [S × JS] + ER(S), c being a small parameter, describing the nonlinear dynamics of the magnetization field in a one-dimensional ferromagnet with a biaxial anisotropy, are analysed. Perturbation theory based on the Riemarm problem is constructed for studying the influence of small perturbations on the dynamics of domai...

We consider the solution to Burger’s equation coupled to a stochastic noise in Ito’s sense. The main random properties of the wave are determined. The solution is related to a deterministic problem with a rescaled diffusion coefficient. Depending on the value of a parameter, the initial value problem may be ill posed, well posed up to an explosion time, or well posed for all time. Traveling wav...