A class of time dependent solutions to (3 + 1) Einstein–Maxwell-dilaton theory with attractive electric force is found from Einstein–Weyl structures in (2+1) dimensions corresponding to dispersionless Kadomtsev–Petviashvili and SU(∞) Toda equations. These solutions are obtained from time–like Kaluza–Klein reductions of (3 + 2) solitons. ∗email [email protected]

We consider the vectorial approach to the binary Darboux transformations for the Kadomtsev-Petviashvili hierarchy in its ZakharovShabat formulation. We obtain explicit formulae for the Darboux transformed potentials in terms of Grammian type determinants. We also study the n-th Gel’fand-Dickey hierarchy introducing spectral operators and obtaining similar results. We reduce the above mentioned ...

For a rather general class of equations of Kadomtsev-Petviashvili (KP) type, we prove that the zero-mass (in x) constraint is satisfied at any non zero time even if it is not satisfied at initial time zero. Our results are based on a precise analysis of the fundamental solution of the linear part and its anti x-derivative.

The key objective of this paper is to construct exact traveling wave solutions the conformable time second integro-differential Kadomtsev–Petviashvili (KP) hierarchy equation using Exp-function method and (2 + 1)-dimensional partial Jaulent–Miodek (JM) evolution utilizing generalized Kudryashov method. These two problems involve derivative with respect time. Initially, equations can be converte...

in this paper, we develop an efficient legendre wavelets collocation method for well known time-fractional heat equation. inthe proposed method, we apply operational matrix of fractionalintegration to obtain numerical solution of the inhomogeneoustime-fractional heat equation with lateral heat loss and dirichletboundary conditions. the power of this manageable method isconfirmed. moreover, the ...

This paper proposes a new computational scheme for approximating variable-order fractional integral operators by means of finite element scheme. This strategy is extended to approximate the solution of a class of variable-order fractional nonlinear systems with time-delay. Numerical simulations are analyzed in the perspective of the mean absolute error and experimental convergence order. To ill...

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

n this paper, at first the  concept of caputo fractionalderivative is generalized on time scales. then the fractional orderdifferential equations are introduced on time scales. finally,sufficient and necessary conditions are presented for the existenceand uniqueness of solution of initial valueproblem including fractional order differential equations.

In this article, the generalized Jacobi elliptic function expansion method with four new functions was used to fractional (3 + 1)-dimensional Kadomtsev–Petviashvili (GFKP) equation Atangana-Baleanu-Riemann derivative, and abundant types of analytical solutions GFKP were obtained. It is well known that there a tight connection between symmetry travelling wave solutions. Most existing techniques ...