A method is given for finding the shifts in position of the solitons for the case of nonzero reflection coefficient. Expressions for boost generators in terms of scattering data play a prominent role in the analysis. Phase-shift formulas which show the effect of the radiation component on the soliton motion are deduced for the nonlinear Schrodinger equation, the Korteweg —de Vries equation, and...

Based on the local fractional derivative, a new Klein-Fock-Gordon equation is derived in this paper for first time. A simple method namely Yang?s special function used to seek non-differentiable exact solutions. The whole calculation process strongly shows that proposed and effective, can be applied investigate solu?tions of other PDE.

In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM).Comparisons are made between the Adomian decomposition method (ADM), the exact solution and homotopy analysis method. The results reveal that the proposed method is very effective and simple.

We study the scattering theory for the coupled KleinGordon-Schrödinger equation with the Yukawa type interaction in two space dimensions. The scattering problem for this equation belongs to the borderline between the short range case and the long range one. We show the existence of the wave operators to this equation without any size restriction on the Klein-Gordon component of the final state.

In this article, we study the oscillation of solutions to a nonlinear forced fractional differential equation. The fractional derivative is defined in the sense of the modified Riemann-Liouville derivative. Based on a transformation of variables and properties of the modified Riemann-liouville derivative, the fractional differential equation is transformed into a second-order ordinary different...

A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By the space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Fell...

We make use of fractional derivative, recently proposed by Caputo and Fabrizio, to modify the nonlinear Nagumo diffusion and convection equation. The proposed fractional derivative has no singular kernel considered as a filter. We examine the existence of the exact solution of the modified equation using the method of fixed-point theorem. We prove the uniqueness of the exact solution and presen...

We prove the global well-posedness and we study the linear response for a system of two coupled equations composed of a Dirac equation for an infinite rank operator and a nonlinear wave or Klein-Gordon equation.

In this paper, we consider the Cauchy problem for Klein-Gordon equation with a cubic convolution nonlinearity in R. Making use of Bourgain’s method in conjunction with precise Strichartz estimates of S.Klainerman and D.Tataru, we establish the Hs-global well-posedness with s < 1 of the Cauchy problem for the cubic convolution defocusing Klein-Gordon-Hartree equation, inspired by I. Gallagher an...