In this paper, based on the close relationship between the Weierstrass elliptic function ℘(ξ; g2, g3)(g2, g3, invariants) and nonlinear ordinary differential equation, a Weierstrass elliptic function expansion method is developed in terms of the Weierstrass elliptic function instead of many Jacobi elliptic functions. The mechanism is constructive and can be carried out in computer with the aid ...

In the first part of this work we study local well-posedness dispersive equations in weighted spaces $$H^s({\mathbb {R}})\cap L^2(|x|^{2b}dx)$$ . We then apply our results for several models such as Hirota-Satsuma system, OST equation, Kawahara equation and a fifth-order model. Using these results, second is devoted to obtain related blow up system.

In this paper, an efficient algorithm of logarithmic transformation to Hirota bilinear form of the KdV-type bilinear equation is established. In the algorithm, some properties of Hirota operator and logarithmic transformation are successfully applied, which helps to prove that the linear terms of the nonlinear partial differential equation play a crucial role in finding the Hirota bilinear form...

The paper presents two results. First it is shown how the discrete potential modified KdV equation and its Lax pairs in matrix form arise from the Hirota–Miwa equation by a 2-periodic reduction. Then Darboux transformations and binary Darboux transformations are derived for the discrete potential modified KdV equation and it is shown how these may be used to construct exact solutions.

this paper studies the existence of solutions for acoupled system of nonlinear fractional differential equations. newexistence and uniqueness results are established using banach fixedpoint theorem. other existence results are obtained using schaeferand krasnoselskii fixed point theorems. some illustrative examplesare also presented.

The nonlocal symmetry of the Drinfeld–Sokolov–Satsuma–Hirota system is obtained from the known Lax pair, and infinitely many nonlocal symmetries are given by introducing the internal parameters. Then the nonlocal symmetry is localized to a prolonged system by introducing suitable auxiliary dependent variables. By applying the classical Lie symmetry method to this prolonged system, two main resu...

In this article, we investigate the utilization of Riemann–Liouville’s fractional integral and Caputo derivative in application Optimal Auxiliary Function Method (OAFM). The extended OAFM is employed to analyze non-linear coupled ITO systems KDV systems, which feature equations a order time. We compare results obtained for system with those derived from Homotopy Perturbation (HPM) New Iterative...

Abstract In this article, through the Hirota bilinear method and long wave limit method, based on N-solitons, we construct multiple lump solutions of generalized (3+1)-dimensional Hirota–Satsuma–Ito equation. Furthermore, to enhance our understanding obtained, further elucidate physical implications these with three-dimensional two-dimensional graphs. The obtained might have practical applicati...

The periodic wave solution for the generalized Hirota-Satsuma system was obtained by using the F-expansion method which can be thought of as a generalization of the Jacobi elliptic function method proposed recently. The Adomian decomposition method is used to solve the same system numerically and the approximate solution is compared with the exact solution. Moreover, we analyze the absolute err...