The Kadomtsev-Petviashvili (KP) equation is known to admit exact, quasiperiodic solutions that can be written in terms of Riemann theta functions, with a nite number of phases in each solution. In this paper, we propose a method to solve the initial-value problem for the KP equation, for initial data taken from this class of quasiperiodic functions.

We employ the idea of Hirota’s bilinear method, to obtain some new exact soliton solutions for high nonlinear form of (2+1)-dimensional potential Kadomtsev-Petviashvili equation. Multiple singular soliton solutions were obtained by this method. Moreover, multiple singular soliton solutions were also derived. Keywords—Hirota bilinear method, potential KadomtsevPetviashvili equation, Multiple sol...

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...

In this paper, we find the exact solutions of some nonlinear evolution equations by using ( ′ G )expansion method. Four nonlinear models of physical significance i.e. the symmetric regularized longwave equation, the Klein-Gordon-Zakharov equations, the Burgers-Kadomtsev-Petviashvili equation and the nonlinear Schrödinger equation with a cubic nonlinearity are considered and obtained their exact...

In this paper, we extend the Petviashvili method (PM) to fractional nonlinear Schrödinger equation (fNLSE) for construction and analysis of its soliton solutions. We also investigate temporal dynamics stabilities solutions fNLSE by implementing a spectral method, in which fractional-order derivatives are computed using FFT (Fast Fourier Transform) routines, time integration is performed 4th ord...

Article history: Received 31 March 2015 Received in revised form 18 June 2015 Accepted 30 June 2015 Available online 2 July 2015 Communicated by R. Wu

We present a method to construct inverse scattering problems for integrable nonlinear evolution equations in the two-spatial dimension. The temporal component is the adjoint of the linearized equation and the spatial component is a partial differential equation with respect to the spatial variables. Although this idea has been known for the one-spatial dimension for some time, it is the first t...