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On Non-point Invertible Transformations of Difference and Differential-difference Equations
Exactly Solvable and Integrable Systems (nlin.SI)
2010/11/10
Non-point invertible transformations are completely described for difference equations on the quad-graph and for their differential-difference analogues. As an illustration, these transformations are ...
On the classification of scalar evolutionary integrable equations in $2+1$ dimensions
On the classification scalar evolutionary integrable equations $2+1$ dimensions
2010/11/10
We consider evolutionary equations of the form $u_t=F(u, w)$ where $w=D_x^{-1}D_yu$ is the nonlocality, and the right hand side $F$ is polynomial in the derivatives of $u$ and $w$. The recent paper \c...
Bidifferential calculus, matrix SIT and sine-Gordon equations
Bidifferential calculus matrix SIT sine-Gordon equations
2010/11/10
We express a matrix version of the self-induced transparency (SIT) equations in the bidifferential calculus framework. An infinite family of exact solutions is then obtained by application of a genera...
The Gould-Hopper Polynomials in the Novikov-Veselov equation
Gould-Hopper Polynomials Novikov-Veselov equation
2010/11/10
We use the Gould-Hopper (GH) polynomials to investigate the Novikov-Veselov (NV) equation. The root dynamics of the $\sigma$-flow in the NV equation is studied using the GH polynomials and then the L...
On a Novel Class of Integrable ODEs Related to the Painlevé Equations
Painlev´ e equation conjugate Painlev´ e equation
2010/12/16
One of the authors has recently introduced the concept of conju-gate Hamiltonian systems: the solution of the equation h = H(p, q, t),where H is a given Hamiltonian containing t explicitly, yields the...
Multisummability of unfoldings of tangent to the identity diffeomorphisms
resonant diffeomorphism bifurcation theory asymptotic expansions Gevrey
2010/12/8
We prove the multisummability of the infinitesimal generator of unfoldings of finite codimension tangent to the identity 1-dimensional local complex analytic diffeomorphisms. We also prove the multisu...
Separation of variables for symplectic characters
Separation of variables symplectic characters
2010/12/6
We perform separation of variables for the symplectic Weyl character using Sklyanin’s scheme. Viewing the characters as eigenfunctions of a quantum integrable system, we explicitlyconstruct the separa...
We establish a decoupling result for the P and S waves of linear, isotropic elasticity, in the setting of twice-differentiable Lam´e parameters.
On the rate of convergence of weak Euler approximation for non-degenerate SDEs
L´ evy processes stochastic differential equations
2010/12/10
The paper estimates the rate of convergence of the weak Euler approximation for solutions to SDEs driven by point and martingale measures, with H¨older continuous coefficients. The equation considered...
Non-uniform dependence on initial data for the CH equation on the line
CH equation integrable non-periodic Cauchy problem Sobolev spaces
2010/12/10
For s > 3=2 two sequences of CH solutions living in a bounded set of the Sobolev space Hs(R) are constructed, whose distance at the initial time is converging to zero while at any later time is bounde...
Positive periodic solutions of singular systems of first order ordinary differential equations
Periodic solutions singular system Krasnoselskii fixed point
2010/12/10
The existence and multiplicity of positive periodic solutions for first non-autonomous singular systems are established with superlinearity or sublinearity assumptions atinfinity for an appropriately ...
A discontinuous Galerkin method for the Vlasov-Poisson system
Discontinuous Galerkin method Vlasov-Poisson system
2010/12/15
A discontinuous Galerkin method for approximating the Vlasov-Poisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in th...
On long-time decay for modified Klein-Gordon equation
Klein-Gordon equation relativistic equations resolvent spectral representa-tion
2010/12/6
We obtain a dispersive long-time decay in weighted energy norms for solutions of the Klein-Gordon equation in a moving frame. The decay extends the results of Jensen, Kato and Murata for the equations...
Preliminary group classification for generalized inviscid Burger's equation
Burgers’ equation Equivalence transformations Lie symmetries
2010/12/9
Preliminary group classification for a class of generalized inviscid Burger’s equa-tions in the general form ut+g(x, u)ux = f(x, u) is given and additional equivalence transformations are found. Adduc...
Examples of Minimal Diffeomorphisms on $t^{2}$ Semiconjugated to an Ergodic Translation
Examples of Minimal Diffeomorphisms Ergodic Translation
2010/11/29
We prove that for every ǫ > 0 there exists a minimal diffeomorphism f : T2 ! T2 of class C3−ǫ and semiconjugate to an ergodic traslation, and have the following properties: zero entrop...