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...

In this paper we study weak continuity of the dynamical systems for the KdV equation in H−3/4(R) and the modified KdV equation in H1/4(R). This topic should have significant applications in the study of other properties of these equations such as finite time blow-up and asymptotic stability and instability of solitary waves. The spaces considered here are borderline Sobolev spaces for the corre...

We produce soliton and similarity solutions of supersymmetric extensions of Burgers, Korteweg–de Vries and modified KdV equations. We give new representations of the τ -functions in Hirota bilinear formalism. Chiral superfields are used to obtain such solutions. We also introduce new solitons called virtual solitons whose nonlinear interactions produce no phase shifts.

It is well known that x-translation and t-translation invariance of (1) leads to the following symmetries: ux, ut of the KdV equation (1). In order to find more generalized symmetries, the concepts of recursion operators or strong symmetries, and hereditary symmetries were introduced by Olver and Fuchssteiner and used to find these symmetries [1, 2]. Furthermore, Galilean invariance of the KdV ...

The KdV equation has many applications in mechanics and wave dynamics. Therefore, researchers are carrying out work to develop analyze modified generalized forms of the standard equation. In this paper, we inspect KdV-mKdV equation, which is a form ordinary We use fractional operator Caputo sense examine some theoretical results concerned with solution’s existence, uniqueness, stability. employ...

All the equations of the KdV hierarchy share many common features, like single and multiple soliton solutions, singular algebraic potentials, etc.; in particular the phase shifts for solitonsoliton scattering are all the same in the chain KdV1, KdV2, etc., depending only on the momenta. We exhibit the reason for this behaviour: as these equations are originated as isopectral deformations of the...

In this paper, the variational iteration method (VIM) is reintroduced with Laplace transforms and the Padé technique treatment to obtain closed form solutions of nonlinear equations. Some examples, including the coupled Burger’s equation, compacton k(n, n) equation, Zakharov–Kuznetsov Zk(n, n) equation, and KdV and mKdV equations are given to show the effectiveness of the coupled VIM–Laplace–Pa...