相关论文: Complex version KdV equation and the periods solut…
We show that the KdV and the NLS equations are tri-Hamiltonian systems. We obtain the third Hamiltonian structure for these systems and prove Jacobi identity through the method of prolongation. The compatibility of the Hamiltonian…
A few 2+1-dimensional equations belonging to the KP and modified KP hierarchies are shown to be sufficient to provide a unified picture of all the integrable cases of the cubic and quartic H\'enon-Heiles Hamiltonians.
It is shown that one system of coupled KdV equations, found in J. Nonlin. Math. Phys., 1999, Vol.6, Nr.3, 255--262 [arXiv:solv-int/9901005] to possess the Painlev\'e property, is integrable but not new.
The stability of the elliptic solutions to the defocusing complex modified Korteweg-de Vries (cmKdV) equation is studied. The orbital stability of the cmKdV equation was established in [19] when the periodic orbits do not oscillate around…
We show that a new integrable two-component system of KdV type studied by Karasu (Kalkanli) et al. (arXiv: nlin.SI/0203036) is bihamiltonian, and its recursion operator, which has a highly unusual structure of nonlocal terms, can be written…
We study the existence of a periodic solution for a differential equation with distributed delay. It is shown that, for a class of distributed delay diferential quations, a symmetric period 2 solution, where the period is twice the maximum…
A general structure is developed from which a system of integrable partial difference equations is derived generalising the lattice KdV equation. The construction is based on an infinite matrix scheme with as key ingredient a (formal)…
In this paper, we study periodic wave solutions of coupled KdV-type equations. We present a numerical process to calculate the $N$-periodic waves based on the direct method of calculating periodic wave solutions proposed by Akira Nakamura.…
In this work we generalize ${\cal M}_{2}$-extension that has been introduced recently. For illustration we use the KdV equation. We present five different ${\cal M}_{3}$-extensions of the KdV equation and their recursion operators. We give…
Some types of coupled Korteweg de-Vries (KdV) equations are derived from an atmospheric dynamical system. In the derivation procedure, an unreasonable $y$-average trick (which is usually adopted in literature) is removed. The derived models…
We consider equations in the modified KdV (mKdV) hierarchy and make use of the Miura transformation to construct expressions for their Lax pair. We derive a Lagrangian-based approach to study the bi-Hamiltonian structure of the mKdV…
A new iterative method is developed to numerically calculate the periodic, matched beam envelope solution of the coupled Kapchinskij-Vladimirskij (KV) equations describing the transverse evolution of a beam in a periodic, linear focusing…
In this paper, we will consider a kind of infinite dimensional Hamiltonian system(HS), by the method of saddle point reduction, topology degree and the index, we will get the existence of periodic solution for (HS).
We prove the existence of Cantor families of small amplitude, linearly stable, quasi-periodic solutions of quasi-linear autonomous Hamiltonian generalized KdV equations. We consider the most general quasi-linear quadratic nonlinearity. The…
Lie symmetry method is applied to investigate symmetries of the combined KdV-nKdV equation, that is a new integrable equation by combining the KdV equation and negative order KdV equation. Symmetries which are obtained in this article, are…
We introduce an exponential-type time-integrator for the KdV equation and prove its first-order convergence in $H^1$ for initial data in $H^3$. Furthermore, we outline the generalization of the presented technique to a second-order method.
The KdV equation can be derived in the shallow water limit of the Euler equations. Over the last few decades, this equation has been extended to include higher order effects. Although this equation has only one conservation law, exact…
A generalized KdV equation is formulated as an exterior differential system, which is used to determine the prolongation structure of the equation. The prolongation structure is obtained for several cases of the variable powers, and…
\begin{abstract} We show that if the initial profile $q\left( x\right) $ for the Korteweg-de Vries (KdV) equation is essentially semibounded from below and $\int^{\infty }x^{5/2}\left\vert q\left( x\right) \right\vert dx<\infty,$ (no decay…
The purpose of the paper is to show that, in low dimensions, the WDVV equations are bi-Hamiltonian. The invariance of the bi-Hamiltonian formalism is proved for $N=3$. More examples in higher dimensions show that the result might hold in…