相关论文: The homogeneous balance method, Lax pair, Hirota t…
In this paper, we use the homogeneous balance(HB) method is used to construct function transformation to solve the nonlinear development equation||Fisher-Kolomogror-Pertrovskii-Piskmov equation (FKPP equation), then the exact solution of…
In this paper, two kinds of the exact singular solutions are obtained by the improved homogeneous balance (HB) method and a nonlinear transformation. The two exact solutions show that special singular wave patterns exists in the classical…
We study to unify soliton systems, KdV/mKdV/sinh-Gordon, through SO(2,1) $\cong$ GL(2,$\mathbb R$) $\cong$ M\"{o}bius group point of view, which might be a keystone to exactly solve some special non-linear differential equations. If we…
The nonlocal symmetry of the generalized fifth order KdV equation (FOKdV) is first obtained by using the related Lax pair and then localized in a new enlarged system by introducing some new variables. On this basis, new Backlund…
In this paper, based on the regular KdV system, we study negative order KdV (NKdV) equations about their Hamiltonian structures, Lax pairs, infinitely many conservation laws, and explicit multi-soliton and multi-kink wave solutions thorough…
We introduced a fifth-order partial differential equation as a generalization of Hirota-Satsuma coupled with KdV system. This equation is investigated based on tanh method. By applying the suitable independent variable in Hirota-Satsuma…
A series of new soliton solutions are presented for the inhomogeneous variable coefficient Hirota equation by using the Riemann Hilbert method and transformation relationship. First, through a standard dressing procedure, the N-soliton…
A general form of the fifth-order nonlinear evolution equation is considered. Helmholtz solution of the inverse variational problem is used to derive conditions under which this equation admits an analytic representation. A Lennard type…
A simplified version of Hirota's method for the computation of solitary waves and solitons of nonlinear PDEs is presented. A change of dependent variable transforms the PDE into an equation that is homogeneous of degree. Solitons are then…
Employing the Lax pairs of the noncommutative discrete potential Korteweg--de Vries (KdV) and Hirota's KdV equations, we derive differential--difference equations that are consistent with these systems and serve as their generalised…
The method of harmonic balance (HB) is a spectrally accurate method used to obtain periodic steady state solutions to dynamical systems subjected to periodic perturbations. We adapt HB to solve for the stress response of the Giesekus model…
A Backlund transformation(BT) and a recurrence formula are derived by the homogeneous balance(HB) method. A initial problem of Burgers equations is reduced to a initial problem of heat equation by the BT, the initial problem of heat…
The N=2 supersymmetric KdV equations are studied within the framework of Hirota's bilinear method. For two such equations, namely $N=2, a=4$ and $N=2, a=1$ supersymmetric KdV equations, we obtain the corresponding bilinear formulations.…
The Hirota bilinear difference equation is generalized to discrete space of arbitrary dimension. Solutions to the nonlinear difference equations can be obtained via B\"acklund transformation of the corresponding linear problems.
For the supersymmetric KdV equation, a proper Darboux transformation is presented. This Darboux transformation leads to the B\"{a}cklund transformation found early by Liu and Xie \cite{liu2}. The Darboux transformation and the related…
Hirota's discrete KdV equation is a well-known integrable two-dimensional partial difference equation regarded as a discrete analogue of the KdV equation. In this paper, we show that a variation of Hirota's discrete KdV equation with an…
An auto-B\"acklund transformation for the quad equation $\mathrm{Q1}_1$ is considered as a discrete equation, called $\mathrm{H2}^a$, which is a so called torqued version of $\mathrm{H2}$. The equations $\mathrm{H2}^a$ and $\mathrm{Q1}_1$…
We consider the resolution of the N=2 supersymmetric KdV equation with a=-2 (SKdV_{a=-2}) from two approaches, the group invariant method (or symmetry reduction) and the Hirota formalism. A bilinear form of the SKdV_{a=-2} equation is…
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…
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…