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The purpose of this paper is to prove that, for a large class of nonlinear evolution equations known as scalar viscous balance laws, the spectral (linear) instability condition of periodic traveling wave solutions implies their orbital…
We argue the integrability of the generalized KdV(GKdV) equation using the Painlev\'e test. For $d( \le 2)$ dimensional space, GKdV equation passes the Painlev\'e test but does not for $d \geq 3$ dimensional space. We also apply the…
A useful semiclassical method to calculate eigenfunctions of the Schroedinger equation is the mapping to a well-known ordinary differential equation, as for example Airy's equation. In this paper we generalize the mapping procedure to the…
We study incremental wave propagation for what is seemingly the simplest boundary value problem, namely that constitued by the plane interface of a semi-infinite solid. With a view to model loaded elastomers and soft tissues, we focus on…
We investigate whether the recently proposed PT-symmetric extensions of generalized Korteweg-de Vries equations admit genuine soliton solutions besides compacton solitary waves. For models which admit stable compactons having a width which…
We introduce a weak transversality condition for piecewise C^{1+\alpha} and piecewise hyperbolic maps which admit a C^{1+\alpha} stable distribution. We show good bounds on the essential spectral radius of the associated transfer operators…
A new integrable class of Davey--Stewartson type systems of nonlinear partial differential equations (NPDEs) in 2+1 dimensions is derived from the matrix Kadomtsev--Petviashvili equation by means of an asymptotically exact nonlinear…
In this work we study the integrability of a family of nonlinear oscillators. Dynamical systems from this family appear in different applications from mechanics to chemistry. We propose an approach for finding first integrals and…
We investigate how two finite-amplitude, transverse, plane body waves may be superposed to propagate in a deformed hyperelastic incompressible solid. We find that the equations of motion reduce to a well-determined system of partial…
This paper continues our previous work done in math.AG/0008207 and is an attempt to establish a conceptual framework which generalizes the work of Manin on the relation between non-linear second order ODEs of type Painleve VI and integrable…
The Henon-Heiles system in the general form has been considered. In a nonintegrable case with the help of the Painleve test new solutions have been found as formal Laurent or Puiseux series, depending on three parameters. One of parameters…
The Pavlov equation is one of the simplest integrable systems of vector fields arising from various problems of mathematical physics and differential geometry which are intensively studied in recent literature. In this report, solving a…
This short review is an introduction to a great variety of methods, the collection of which is called the Painlev\'e analysis, intended at producing all kinds of exact (as opposed to perturbative) results on nonlinear equations, whether…
We present an N=2-supersymmetric mechanical system whose bosonic sector, with two degrees of freedom, stems from the reduction of an SU(2) Yang-Mills theory with the assumption of spatially homogeneous field configurations and a particular…
In this paper we study the integrability of a class of Gross-Pitaevskii equations managed by Feshbach resonance in an expulsive parabolic external potential. By using WTC test, we find a condition under which the Gross-Pitaevskii equation…
We apply various conventional tests of integrability to the supersymmetric nonlinear Schr\"odinger equation. We find that a matrix Lax pair exists and that the system has the Painlev\'e property only for a particular choice of the free…
The procedure of the "quantum" linearization of the Hamiltonian ordinary differential equations with one degree of freedom is introduced. It is offered to be used for the classification of integrable equations of the Painleve type. By this…
In the Painleve analysis of nonintegrable partial differential equations one obtains differential constraints describing the movable singularity manifold. We show, for a class of n-dimensional wave equations, that these constraints have a…
We propose an EPR inequality based on an entropic uncertainty relation for complementary continuous variable observables. This inequality is more sensitive than the previously established EPR inequality based on inferred variances, and…
We derive differential equations for multiplicative statistics of the Bessel determinantal point process depending on two parameters. In particular, we prove that such statistics are solutions to an integrable nonlinear partial differential…