Related papers: The Painlev\'e Test of Higher Dimensional KdV Equa…
We prove that one system of coupled KdV equations, claimed by Hirota, Hu, and Tang to pass the Painleve test for integrability, actually fails the test at the highest resonance of the generic branch and therefore must be non-integrable.
The general KdV equation (gKdV) derived by T. Chou is one of the famous (1+1) dimensional soliton equations with variable coefficients. It is well-known that the gKdV equation is integrable. In this paper a higher-dimensional gKdV equation,…
The Painlev\'{e} property of coupled, non-autonomous Korteweg-de Vries (KdV) type of systems is studied. The conditions under which the systems pass the Painlev\'{e} test for integrability are obtained. For some of the integrable cases,…
A (2+1)-dimensional perturbed KdV equation, recently introduced by W.X. Ma and B. Fuchssteiner, is proven to pass the Painlev\'e test for integrability well, and its 4$\times $4 Lax pair with two spectral parameters is found. The results…
The Painlev\'e analysis of a generic multiparameter N=2 extension of the Korteweg-de Vries equation is presented. Unusual aspects of the analysis, pertaining to the presence of two fermionic fields, are emphasized. For the general class of…
A new three-dimensional second-order nonlinear wave equation is introduced which passes the Painleve test for integrability and possesses KdV-type multisoliton solutions. Lax integrability of this equation remains unknown.
We present some nonlinear partial differential equations in 2+1-dimensions derived from the KdV Equation and its symmetries. We show that all these equations have the same 3-soliton structures. The only difference in these solutions are the…
The integrability of a four-dimensional sixth-order bilinear equation associated with the exceptional affine Lie algebra $D_4^{(1)}$ is studied by means of the singularity analysis. This equation is shown to pass the Painlev\'{e} test in…
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.
It is shown that the system of two coupled Korteweg-de Vries equations passes the Painlev\'e test for integrability in nine distinct cases of its coefficients. The integrability of eight cases is verified by direct construction of Lax…
A method for carrying out the Painleve test in superspace is proposed. The method is then applied to the one-parameter N=1 supersymmetric extensions of the KdV equation.
We consider two multi-dimensional generalisations of the dispersionless Kadomtsev-Petviashvili (dKP) equation, both allowing for arbitrary dimensionality, and non-linearity. For one of these generalisations, we characterise all solutions…
We investigate the integrability of Nonlinear Partial Differential Equations (NPDEs). The concepts are developed by firstly discussing the integrability of the KdV equation. We proceed by generalizing the ideas introduced for the KdV…
The three-dimensional Armbruster Guckenheimer Kim galactic potential in the general form is considered. The integrability of this problem is performed by using the Painlev\'e analysis. We report three cases of integrability, exact integrals…
Using the Painlev\'e--Kovalevskaya test, we find several new matrix generalizations of the Painlev\'e-4 equation. Some limiting transitions reduce them to known matrix Painlev\'e-2 equations.
The Painlev\'e property for a (2+1)-dimensional Korteweg-de Vries (KdV) extension, the combined KP3 (Kadomtsev- Petviashvili) and KP4 (cKP3-4) is proved by using Kruskal's simplification. The truncated Painlev\'e expansion is used to find…
The (2+1)-dimensional spherical Kadomtsev-Petviashvili (SKP) equation of J.-K. Xue [Phys. Lett. A 314:479-483 (2003)] fails the Painleve test for integrability at the highest resonance, where a nontrivial compatibility condition for…
We investigate the Painleve analysis for a (2+1) dimensional Camassa-Holm equation. Our results show that it admits only weak Painleve expansions. This then confirms the limitations of the Painleve test as a test for complete integrability…
In this paper we propose a geometric approach to study Painlev\'e equations appearing as constrained systems of three first-order ordinary differential equations. We illustrate this approach on a system of three first-order differential…
After a brief introduction to the Painlev\'{e} property for ordinary differential equations, we present a concise review of the various methods of singularity analysis which are commonly referred to as Painlev\'{e} tests. The tests are…