Related papers: Solution of the dispersionless Hirota equations
Using the technique of labeled operators, compact explicit expressions are given for all traced heat kernel coefficients containing zero, two, four and six covariant derivatives, and for diagonal coefficients with zero, two and four…
Nonlinear reaction-diffusion systems are known to exhibit very many novel spatiotemporal patterns. Fisher equation is a prototype of diffusive equations. In this contribution we investigate the integrability properties of the generalized…
Asymptotic expansions of Green functions and spectral densities associated with partial differential operators are widely applied in quantum field theory and elsewhere. The mathematical properties of these expansions can be clarified and…
A multidimensionally consistent generalisation of Hirota's discrete KdV equation is proposed, it is a quad equation defined by a polynomial that is quadratic in each variable. Soliton solutions and interpretation of the model as…
We study integrable non-degenerate Monge-Ampere equations of Hirota type in 4D and demonstrate that their symmetry algebras have a distinguished graded structure, uniquely determining the equations. This is used to deform these heavenly…
In this paper, we study the full asymptotic expansion of the partition functions of determinantal point processes defined on a polarized K\"ahler manifold. We show that the coefficients of the expansion are given by geometric functionals on…
Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…
Interpretation of dispersionless integrable hierarchies as equations of coisotropic deformations for certain algebras and other algebraic structures like Jordan triple systInterpretation of dispersionless integrable hierarchies as equations…
We consider fractional diffusion equation with the distributed order Caputo derivative. We prove existence of a weak and regular solution for general uniformly elliptic operator under the assumption that the weight function is only…
We provide a general theoretical framework allowing us to extend the classical Lie theory for partial differential equations to the case of equations of fractional order. We propose a general prolongation formula for the study of Lie…
This article aims to develop a direct numerical approach to solve the space-fractional partial differential equations (PDEs) based on a new differential quadrature (DQ) technique. The fractional derivatives are approximated by the weighted…
The Fast Diffusion Equation (FDE) $u_t= \Delta u^m$, with $m\in (0,1)$, is an important model for singular nonlinear (density dependent) diffusive phenomena. Here, we focus on the Cauchy-Dirichlet problem posed on smooth bounded Euclidean…
We analyze solvability of a special form of distributed order fractional differential equations within the space of tempered distributions supported by the positive half-line.
The dispersionless KP and Toda hierarchies possess an underlying twistorial structure. A twistorial approach is partly implemented by the method of Riemann-Hilbert problem. This is however still short of clarifying geometric ingredients of…
In this paper we show several connections between special functions arising from generalized COM-Poisson-type statistical distributions and integro-differential equations with varying coefficients involving Hadamard-type operators. New…
We define an integral, the distributional integral of functions of one real variable, that is more general than the Lebesgue and the Denjoy-Perron-Henstock-Kurzweil integrals, and which allows the integration of functions with…
The object of this paper is to present a computable solution of a fractional partial differential equation associated with a Riemann-Liouville derivative of fractional order as the time-derivative and Riesz-Feller fractional derivative as…
This paper is devoted to studying propagation phenomena in integro-differential equations with a weakly degenerate non-linearity. The reaction term can be seen as an intermediate between the classical logistic (or Fisher-KPP) non-linearity…
We give a recursive formula for an expansion of a solution of a general non-autonomous polynomial differential equation. The formula is given on the algebraic level with a use of shuffle product. This approach minimizes the number of…
The extended de Finetti theorem characterizes exchangeable infinite random sequences as conditionally i.i.d. and shows that the apparently weaker distributional symmetry of spreadability is equivalent to exchangeability. Our main result is…