In this paper, we establish exact solutions for the timefractional Klein-Gordon equation, and the time-fractional HirotaSatsuma coupled KdV system. The Hes semi-inverse and the Kudryashov methods are used to construct exact solutions of these equations. We apply Hes semi-inverse method to establish a variational theory for the time-fractional Klein-Gordon equation, and the timefractional Hirota...

In this paper, the ( / ) G G  -expansion method is extended to solve fractional differential equations in the sense of modified Riemann-Liouville derivative. Based on a nonlinear fractional complex transformation, certain fractional partial differential equations can be turned into ordinary differential equations of integer order. For illustrating the validity of this method, we apply it to fi...

Abstract In [1] Varsha and Jaferi proposed an iterative method for solving nonlinear functional equations, viz. nonlinear Voltera integral equations, algebraic equations and system of ordinary differential equations. Then Sachin and Varsha [2] implemented this method to solve linear and nonlinear partial differential equations of integer and fractional order. The aim of this article is to propo...

In this paper, the lattice Boltzmann method for convectiondiffusion equation with source term is applied directly to solve some important nonlinear complex equations, including nonlinear Schrödinger (NLS) equation, coupled NLS equations, Klein-Gordon equation and coupled Klein-Gordon-Schrödinger equations, by using complex-valued distribution function and relaxation time. Detailed simulations o...

With the help of the complex structure and the wave operator of the nonlinear classical Klein-Gordon equation with the interaction u4 we define the Wick kernel of the interacting quantum field in four-dimensional space-time and consider its properties. In particular, the diagonal of this Wick kernel is (real) solutions of the classical nonlinear Klein-Gordon equation with the interaction u4.

We study global dynamics for the focusing nonlinear Klein-Gordon equation with the energy-critical nonlinearity in two or higher dimensions when the energy equals the threshold given by the ground state of a mass-shifted equation, and prove that the solutions are divided into scattering and blowup. In short, the Kenig-Merle scattering/blowup dichotomy [10, 11] extends to the threshold energy in...

we develope a numerical method based on b-spline collocation method to solve linear klein-gordon equation. the proposed scheme is unconditionally stable. the results of numerical experiments have been compared with the exact solution to show the efficiency of the method computationally. easy and economical implementation is the strength of this approach.