in recent years, there has been greater attempt to find numerical solutions of differential equations using wavelet's methods. the following method is based on vector forms of haar-wavelet functions. in this paper, we will introduce one dimensional haar-wavelet functions and the haar-wavelet operational matrices of the fractional order integration. also the haar-wavelet operational matrice...

We introduce an integrable time-discretized version of the classical CalogeroMoser model, which goes to the original model in a continuum limit. This discrete model is obtained from pole solutions of a discretized version of the Kadomtsev-Petviashvili equation, leading to a finite-dimensional symplectic mapping. Lax pair, symplectic structure and sufficient set of invariants of the discrete Cal...

In this paper, the space-time Riesz fractional partial differential equations with periodic conditions are considered. The equations are obtained from the integral partial differential equation by replacing the time derivative with a Caputo fractional derivative and the space derivative with Riesz potential. The fundamental solutions of the space Riesz fractional partial differential equation (...

In this paper, a new (2 + 1)-dimensional nonlinear evolution equation is investigated. This called the Kadomtsev–Petviashvili–Sawada–Kotera–Ramani equation, which can be seen as two-dimensional extension of Korteweg–de Vries–Sawada–Kotera–Ramani equation. By means Hirota’s bilinear operator and binary Bell polynomials, form Bäcklund transformation are obtained. Furthermore, by application Hopf-...

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.

A generalized Kadomtsev-Petviashvili equation, describing water waves in oceans of varying depth, density and vorticity is discussed. A priori, it involves 9 arbitrary functions of one, or two variables. The conditions are determined under which the equation allows an infinite dimensional symmetry algebra. This algebra can involve up to three arbitrary functions of time. It depends on precisely...

Abstract. We show that a monic polynomial in a discrete variable n, with coefficients depending on time variables t1, t2, . . . is a τ -function for the discrete Kadomtsev-Petviashvili hierarchy if and only if the motion of its zeros is governed by a hierarchy of Ruijsenaars-Schneider systems. These τ -functions were considered in [10], where it was proved that they parametrize rank one solutio...