By using disipative version of the second and the third members of AKNS hierarchy, a new method to solve 2+1 dimensional KadomtsevPetviashvili (KP-II) equation is proposed. We show that dissipative solitons (dissipatons) of those members give rise to the real solitons of KP-II. From the Hirota bilinear form of the SL(2,R) AKNS flows, we formulate a new bilinear representation for KP-II, by whic...

In this paper, based on the nonlinear fractional equations proposed by Ablowitz, Been, and Carr in sense of Riesz derivative, we explore coupled Hirota equation give its explicit form. Unlike previous equations, type is integrable. Therefore, obtain $n$-soliton solutions inverse scattering transformation reflectionless case. particular, analyze one- two-soliton prove that can also be regarded a...

In this article, we use the homotopy perturbation method and Adomian decomposition with Yang transformation to discover analytical solution time-fractional coupled Schrödinger–KdV equation. Caputo sense, fractional derivatives are described. A convergent series is used calculate solutions of PDEs. Analytical results achieved applying techniques numerically calculated represented in form tables ...

We put into practice relatively new analytical techniques, the Shehu decomposition method and iterative transform method, for solving nonlinear fractional coupled Korteweg-de Vries (KdV) equation. The KdV equation has been developed to represent a broad spectrum of physics behaviors evolution association waves. Approximate-analytical solutions are presented in form series with simple straightfo...

Various connections between 2-D gravity and KdV, dKdV, inverse scattering, etc. are established. For KP we show how to extract from the dispersionless limit of the Fay differential identity of Takasaki-Takebe the collection of differential equations for F = log(τ ) which play the role of Hirota type equations in the dispersionless theory. 1. HIROTA EQUATIONS In [7] we showed how second derivati...

This research paper targets the fractional Hirota’s analytical solutions–Satsuma (HS) equations. The conformable derivative is employed to convert system into a with an integer–order. extended simplest equation (ESE) and modified Kudryashov (MKud) methods are used construct novel solutions of considered model. solutions’ accuracy investigated by handling computational Adomian decomposition meth...