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...

We show that for a given holomorphic noncharacteristic surface S ∈ C, and a given holomorphic function on S, there exists a unique meromorphic solution of Burgers’ equation which blows up on S. This proves the convergence of the formal Laurent series expansion found by the Painlevé test. The method used is an adaptation of Nirenberg’s iterative proof of the abstract Cauchy-Kowalevski theorem. A...

The Klein-Gordon equation in D-dimensions for a recently proposed Kratzer potential plus ring-shaped potential is solved analytically by means of the conventional Nikiforov-Uvarov method. The exact energy bound-states and the corresponding wave functions of the Klein-Gordon are obtained in the presence of the noncentral equal scalar and vector potentials. The results obtained in this work are m...

We prove a formula conjectured by Ahrens, Gordon, and McMa-hon for the number of interior points for a point connguration in R d. Our method is to show that the formula can be interpreted as a sum of Euler characteristics of certain complexes associated with the point connguration, and then compute the homology of these complexes. This method extends to other examples of convex geometries. We s...

We study the noncommutative generalization of (euclidean) integrable models in two-dimensions, specifically the sine-and sinh-Gordon and the U (N) principal chiral models. By looking at tree-level amplitudes for the sinh-Gordon model we show that its na¨ıve noncommutative generalization is not integrable. On the other hand, the addition of extra constraints, obtained through the generalization ...

We study the noncommutative generalization of (euclidean) integrable models in two-dimensions, specifically the sine-and sinh-Gordon and the U (N) principal chiral models. By looking at tree-level amplitudes for the sinh-Gordon model we show that its na¨ıve noncommutative generalization is not integrable. On the other hand, the addition of extra constraints, obtained through the generalization ...

This paper presents the formulation of time-fractional Klein-Gordon equation using the Euler-Lagrange variational technique in the Riesz derivative sense and derives an approximate solitary wave solution. Our results witness that He’s variational iteration method was very efficient and powerful technique in finding the solution of the proposed equation. The basic idea described in this paper is...

The one-dimensional quantum sine-Gordon system with a linear spatial modulation is investigated in a special case, β2 =4π. The model is tranformed into a massive Thirring model and then is exactly diagonalized, the energy spetrum of the model is obtained. Our result clearly demonstrates that cancelling the cosine term without any considering is unadvisable. The one-dimensional (1D) quantum sine...