Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili [Kadomtsev BB, Petviashvili VI (1970) Sov Phys Dokl 15:539-541] proposed a two-dimensional nonlinear dispersive wave equation now known as the KP equation. It is well-known that the Wronskian approach to the KP equation provides a method to construct soliton solutions. The regular soliton solution...

Bäcklund transformations, which are relations among solutions of partial differential equations–usually nonlinear–have been found and applied mainly for systems with two independent variables. A few are known for equations like the Kadomtsev-Petviashvili equation [1], which has three independent variables, but they are rare. Wahlquist and Estabrook [2] discovered a systematic method for searchi...

in this paper rationalized haar (rh) functions method is applied to approximate the numerical solution of the fractional volterra integro-differential equations (fvides). the fractional derivatives are described in caputo sense. the properties of rh functions are presented, and the operational matrix of the fractional integration together with the product operational matrix are used to reduce t...

A generalized thermo-elastic diffusion problem in a functionally graded isotropic, unbounded, rotating elastic medium due to a periodically varying heat source in the context of fractional order theory is considered in our present work. The governing equations of the theory for a functionally graded material with GNIII model are established. Analytical solution of the problem is derived in Lapl...

Dynamics and digital circuit implementation of the fractional-order Lorenz system are investigated by employing Adomian decomposition method (ADM). Dynamics of the fractional-order Lorenz system with derivative order and parameter varying is analyzed by means of Lyapunov exponents (LEs), bifurcation diagram, chaos diagram and phase diagram. Results show that the fractional-order Lorenz system h...

In this article, the electro-osmotic flow of Oldroyd-B fluid in a circular micro-channel with slip boundary condition is considered. The corresponding fractional system is represented by using a newly defined time-fractional Caputo-Fabrizio derivative without singular kernel. Closed form solutions for the velocity field are acquired by means of Laplace and finite Hankel transforms. Additionally...

Hervé Leblond, David Kremer, and Dumitru Mihalache Laboratoire de Photonique d’Angers, Université d’Angers, 2 Bd. Lavoisier, 49045 Angers Cedex 01, France Horia Hulubei National Institute for Physics and Nuclear Engineering (IFIN-HH), 407 Atomistilor, Magurele-Bucharest, 077125, Romania Academy of Romanian Scientists, 54 Splaiul Independentei, Bucharest 050094, Romania Abstract By using a reduc...