Related papers: On Negative Order KdV Equations
Within the (2 + 1)-dimensional Korteweg-de Vries equation framework, new bilinear Backlund transformation and Lax pair are presented based on the binary Bell polynomials and gauge transformation. By introducing an arbitrary function, a…
Third order dispersive evolution equations are widely adopted to model one-dimensional long waves and have extensive applications in fluid mechanics, plasma physics and nonlinear optics. Among them are the KdV equation, the Camassa--Holm…
This article is a brief review of the results of studying the collapse of sound waves in media with positive dispersion, which is described in terms of the three-dimensional Kadomtsev-Petviashvili (KP) equation. The KP instability of…
A supersymmetric breaking procedure for $N=1$ Super KdV, using a Clifford algebra, is implemented. Dirac's method for the determination of constraints is used to obtain the Hamiltonian structure, via a Lagrangian, for the resulting…
Assuming that there exist at least two fermionic parameters, the classical N= 1 supersymmetric Korteweg-de Vries (SKdV) system can be transformed to some coupled bosonic systems. The boson fields in the bosonized SKdV (BSKdV) systems are…
We provide conditions for existence of hyperbolic, unbounded periodic and elliptic solutions in terms of Weierstrass $\wp$ functions of both third and fifth-order KdV--BBM (Korteweg-de Vries--Benjamin, Bona \& Mahony) regularized long wave…
Taking the coupled KdV system as a simple example, analytical and nonsingular complexiton solutions are firstly discovered in this letter for integrable systems. Additionally, the analytical and nonsingular positon-negaton interaction…
This manuscript embarks on an in-depth exploration of the modified Korteweg-de Vries (mKdV) equation, with a particular emphasis on unraveling the intricate structure of its infinite symmetries and their physical interpretations. Central to…
The Korteweg-de Vries equation (KdV) and various generalized, most often semi- linear versions have been studied for about 50 years. Here, the focus is made on a quasi-linear generalization of the KdV equation, which has a fairly general…
In natural and social science, many events happened at different space-times may be closely correlated. Two events, A (Alice) and B (Bob) are defined as correlated if one event is determined by another, say, $B=\hat{f} A$ for suitable…
In the paper a new nonlinear equation describing shallow water waves with the topography of the bottom directly taken into account is derived. This equation is valid in the weakly nonlinear, dispersive and long wavelength limit. Some…
The negative order KdV (nKdV) and the modified KdV (nmKdV) equations have two different formulations based on different hierarchy operators. Both equations can be written in terms of a nonlinear differential equation for a field $u(x,t)$…
We consider the soliton solutions of a recently proposed coupled Sasa-Satsuma-mKdV equation using the Kadomtsev-Petviashvili reduction method. The system consists of a complex-valued component coupled with a real-valued one. Under zero or…
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 Darboux transformations for the two boson (TB) hierarchy both in the scalar as well as in the matrix descriptions of the linear equation. While Darboux transformations have been extensively studied for integrable models based on…
We study the dynamics of solitons as solutions to the perturbed KdV (pKdV) equation $\partial_t u = -\partial_x (\partial_x^2 u + 3u^2-bu)$, where $b(x,t) = b_0(hx,ht)$, $h\ll 1$ is a slowly varying, but not small, potential. We option an…
We give a simple geometric interpretation of the mapping of the negative KdV equation as proposed by Qiao and Li {arXiv:1101.1605 [math-ph], Europhys. Lett.,94 (2011) 50003} and the Fuchssteiner equation using geometry of projective…
The Klein-Gordon-Boussinesq (KGB) system is proposed in the literature as a model problem to study the validity of approximations in the long wave limit provided by simpler equations such as KdV, nonlinear Schr\"{o}dinger or Whitham…
The finite element method is applied to obtain numerical solutions to the recently derived nonlinear equation for shallow water wave problem for several cases of bottom shapes. Results for time evolution of KdV solitons and cnoidal waves…
We present Backlund transformations (BTs) with parameter for certain classical integrable n-body systems, namely the many-body generalised Henon-Heiles, Garnier and Neumann systems. Our construction makes use of the fact that all these…