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In this talk, I will review several classes of higher-order generalizations of the integrable Camassa-Holm equation in the Hamiltonian forms. Then, I talk about some new results for one generalized Ca...
In this talk, we investigate the fractalization phenomena for the multi-component systems of the dispersive evolution equations on a bounded interval subject to the periodic boundary conditions. The e...
In this talk, we investigate the revival phenomena for the dispersive evolution equations. Firstly, we study the dispersive quantization phenomena for the multi-component systems of the dispersive evo...
We define a new grading, that we call the "level grading", on the algebra of polynomials generated by the derivatives $u_{k+i}=\partial^{k+i}u/\partial x^{k+i}$ over the ring $K^{(k)}$ of $C^{\infty}$...
Semi-inclusive hadron-production processes are becoming important in high-energy hadron reactions. They are used for investigating properties of quark-hadron matters in heavy-ion collisions, for findi...
Abstract: The hierarchies of evolution equations of classical many-particle systems are formulated as evolution equations in functional derivatives. In particular the BBGKY hierarchy for marginal dist...
A. de Sole, V. G. Kac, and M. Wakimoto have recently introduced a new family of compatible Hamiltonian operators of the form H(N,0) = D2 ◦ ((1/u)◦D)2n ◦D, where N = 2n+3, n = 0, 1, ...
A. de Sole, V. G. Kac, and M. Wakimoto have recently introduced a new family of compatible Hamiltonian operators of the form H(N,0) = D2 ◦ ((1/u)◦D)2n ◦D, where N = 2n+3, n = 0, 1, ...
We obtain a large deviation principle describing the small time asymp-totics of the solution of a stochastic evolution equation with multiplicative noise. Our assumptions are a condition on the linear...
In this article we deal with the approximation of solutions of non-linear evolution equations of the form A(u(t))+f(u(t)) = u′(t), the numerical analysis of solutions to this problems will be performe...
In these notes we review some recent results concerning the derivation of effective equations from first principle quantum dynamics. In particular, we discuss the derivation of the semi-relativistic...
The analysis of evolution equations such as ordinary or partial differential equations often splits into two different directions. One either makes minimal assumptions about their structure and trie...
The analysis of evolution equations such as ordinary or partial differential equations often splits into two different directions. One either makes minimal assumptions about their structure and tries ...
We give a complete point-symmetry classification of all third-order evolution equations of the form $u_t=F(t,x,u,u_x, u_{xx})u_{xxx}+G(t,x,u,u_x, u_{xx})$ which admit semi-simple symmetry algebras and...
We analyze the relationship of generalized conditional symmetries of evolution equations to the formal compatibility and passivity of systems of differential equations as well as to systems of vector ...

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