We prove the nonsqueezing property of the coupled Korteweg-de Vries (KdV) type system. Relying on Gromov’s nonsqueezing theorem for finite dimensional Hamiltonian systems, the argument is to approximate the solutions to the original infinite dimensional Hamiltonian system by a frequency truncated finite dimensional system, and then the nonsqueezing property is transferred to the infinite dimens...

Geometric interpretation of the Hirota equation is presented as equation describing the Laplace sequence of two-dimensional quadrilateral lattices. Different forms of the equation are given together with their geometric interpretation: (i) the discrete coupled Volterra system for the coefficients of the Laplace equation, (ii) the gauge invariant form of the Hirota equation for projective invari...

Bu çalışmada, Drinfeld–Sokolov–Satsuma–Hirota (DSSH) denkleminin yaklaşık çözümü rezidual kuvvet seri metodu (RKSM) kullanılarak elde edildi. Kesirli türevleri karakterize etmek için uyumlu türev yaklaşımı kullanıldı ve farklı operatör değerleri RKSM çözümleri kesin çözümlerle çeşitli tablo grafikler karşılaştırıldı. Sonuçlar; uygulanan tekniğin kullanımının kolay, çok başarılı tutarlı olduğunu...

Conservation laws of the nonlinear Schrödinger equation are studied in the presence of higher-order nonlinear optical effects including the third-order dispersion and the selfsteepening. In a context of group theory, we derive a general expression for infinitely many conserved currents and charges of the coupled higher-order nonlinear Schrödinger equation. The first few currents and charges are...

The paper investigates solutions and Lax pairs through bilinear Backlund transformations for some supersymmetric equations. We derive variety of from the known transformations. Besides, using gauge invariance (super) Hirota derivatives we may get deformed consequently with fermionic parameters. Examples are KdV equation KdV1 equation.

Abstract In this article, we present a fractional Kersten–Krasil’shchik coupled KdV-mKdV nonlinear model associated with newly introduced Atangana–Baleanu derivative of order which uses Mittag-Leffler function as nonsingular and nonlocal kernel. We investigate the behavior multi-component plasma. For effective approach, named homotopy perturbation, transformation approach is suggested. This sch...

The Korteweg-de Vries (KdV) equation is known as a model of long waves in an infinitely long canal over a flat bottom and approximates the two-dimensional water wave problem, which is a free boundary problem for incompressible Euler equation with the irrotational condition. In this paper, we consider the validity of this approximation in the case of presence of surface tension. Moreover, we con...

An analytic study was conducted on coupled partial differential equations. We formally derived new solitary wave solutions of generalized coupled system of Zakharov-Kuznetsov (ZK) and KdV equations by using modified extended tanh method. The traveling wave solutions for each generalized coupled system of ZK and KdV equations are shown in form of periodic, dark, and bright solitary wave solution...

Two different types of N = 1 modified KdV equations are shown to possess N soliton solutions. The soliton solutions of these equations are obtained by casting the equations in the bilinear forms using the supersymmetric extension of the Hirota method. The distinguishing features of the soliton solutions of N = 1 mKdV and N = 1 mKdV B equations are discussed. email: [email protected] email: ...

We extend the action for evolution equations of KdV and MKdV type which was derived in NC] to the case of not periodic, but only equivariant phase space variables, introduced in FV2]. The diierence of these variables may be interpreted as reduced phase space variables via a Marsden-Weinstein reduction where the monodromies play the role of the momentum map. As an example we obtain the doubly di...