Related papers: Comments on the negative grade KdV hierarchy
A new approach to double-sub equation method is introduced to construct novel solutions for the nonlinear partial differential equations. It is applied to the Korteweg-de Vries (KdV) equation and yields new complexiton solutions of both the…
In this paper, we study the properties of a nonlinearly dispersive integrable system of fifth order and its associated hierarchy. We describe a Lax representation for such a system which leads to two infinite series of conserved charges and…
We revisit a non-perturbative space-time curvature theory, underlying a two form U(1) gauge dynamics, on a D4-brane. In particular, two different gauge choices for a two form are explored underlying the dynamics of a geometric torsion in a…
Miura transform is known as the transformation between Korteweg de-Vries equation and modified Korteweg de-Vries equation. Its formal similarity to the Cole-Hopf transform has been noticed. This fact sheds light on the logarithmic type…
We introduce integrable KdV type hierarchy associated naturally with arbitrary semi-simple Frobenius manifold. We present hierarchy in a Lax form and show that it admits bihamiltonian description.
The KdV-equation $u_t = -u_{xxx} + 6uu_x$ on the circle admits a global nonlinear Fourier transform, also known as Birkhoff map, linearizing the KdV flow. The regularity properties of $u$ are known to be closely related to the decay…
Derivation-based differential calculi are of great importance in noncommutative geometry, noncommutative gauge theory and integrable systems. In this paper, we propose the connection and curvature from a class of deformed derivation-based…
We present a new integrable extension of the a=-2, N=2 SKdV hierarchy, with the "small" N=4 superconformal algebra (SCA) as the second hamiltonian structure. As distinct from the previously known N=4 supersymmetric KdV hierarchy associated…
A Dispersive Wave Equation in 2+1 dimensions (2LDW) widely discussed by different authors is shown to be nothing but the modified version of the Generalized Dispersive Wave Equation (GLDW). Using Singularity Analysis and techniques based…
A generalized Nevanlinna function $Q(z)$ with one negative square has precisely one generalized zero of nonpositive type in the closed extended upper halfplane. The fractional linear transformation defined by $Q_\tau(z)=(Q(z)-\tau)/(1+\tau…
In this paper, the compatibility between the gauge transformations and the additional symmetry of the constrained discrete Kadomtsev-Petviashvili hierarchy is given, which preserving the form of the additional symmetry of the cdKP…
The algorithm of finding inverse multivector (MV) numerically and symbolically is of paramount importance in the applied Clifford geometric algebra (GA) $Cl_{p,q}$. The first general MV inversion algorithm was based on matrix representation…
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…
On a closed Riemannian surface $(M,\bar g)$ with negative Euler characteristic, we study the problem of finding conformal metrics with prescribed volume $A>0$ and the property that their Gauss curvatures $f_\lambda= f + \lambda$ are given…
It is shown that the matrix KP hierarchy can yield new integrable equations in $(2+1)$-dimensions along with the corresponding Lax pair. For particular gauge choice this may result derivative and also a higher order nonlinear extension of…
There is a common description of different intrinsic geometric flows in two dimensions using Toda field equations associated to continual Lie algebras that incorporate the deformation variable t into their system. The Ricci flow admits zero…
We introduce a hierarchy of mutually commuting dynamical systems on a finite number of Laurent series. This hierarchy can be seen as a prolongation of the KP hierarchy, or a ``reduction'' in which the space coordinate is identified with an…
We are concerned with the Cauchy problem for the KdV equation for nonsmooth locally integrable initial profiles q's which are, in a certain sense, essentially bounded from below and q(x)=O(e^{-cx^{{\epsilon}}}),x\rightarrow+\infty, with…
The exhaustive group classification of the class of KdV-like equations with time-dependent coefficients $u_t+uu_x+g(t)u_{xxx}+h(t)u=0$ is carried out using equivalence based approach. A simple way for the construction of exact solutions of…
Diagrammatic techniques are invented to implement QCD gauge transformations. These techniques can be used to discover how gauge-dependent terms are cancelled among diagrams to yield gauge-invariant results in the sum. In this way a…