Related papers: Solution of the dispersionless Hirota equations
By the approximation method introduced in \cite{FYW}, the existence and uniqueness are proved for a class of distribution-dependent stochastic functional differential equations (DDSFDEs). Moreover, combining the Harnack and shift-Harnack…
We construct an explicit solution of the Cauchy initial value problem for certain diffusion-type equations with variable coefficients on the entire real line. The corresponding Green function (heat kernel) is given in terms of elementary…
We derive a combinatorial identity which is useful in studying the distribution of Fourier coefficients of L-functions by allowing us to pass from knowledge of moments of the coefficients to the distribution of the coefficients.
A generalized fractional derivative (GFD) definition is proposed in this work. For a differentiable function that can be expanded by Taylor series, we show that D^Elafa*D^Beta f(t)=D^(Elafa+Beta)f(t). GFD is applied for some functions in…
This paper deals with the solution of unified fractional reaction-diffusion systems. The results are obtained in compact and elegant forms in terms of Mittag-Leffler functions and generalized Mittag-Leffler functions, which are suitable for…
Using the discrete Hirota integrability we find the general solution of the full quantum Y-system for the spectrum of anomalous dimensions of operators in the planar AdS5/CFT4 correspondence in terms of Wronskian-like determinants…
We give an integral variational characterization for the speed of fronts of the nonlinear diffusion equation $u_t = u_{xx} + f(u)$ with $f(0)=f(1)=0$, and $f>0$ in $(0,1)$, which permits, in principle, the calculation of the exact speed for…
This paper develops a method for solving free boundary problems for time-homogeneous diffusions. We combine the complete exponential system of solutions for the heat equation, transmutation operators and recently discovered Neumann series…
In view of the usefulness and importance of the kinetic equation in certain physical problems, the authors derive the explicit solution of a fractional kinetic equation of general character, that unifies and extends earlier results.…
We investigate the reductions of dispersionless Harry Dym hierarchy to systems of finitely many partial differential equations. These equations must satisfy the compatibility condition and they are diagonalizable and semi-Hamiltonian. By…
In this work, we introduce a new difference equation which is discrete analogue of Diffusion differential equation and analyze some essential spectral properties, Diffusion difference operator is self-adjoint, eigenvalues of this problem…
The solvability of a delay differential equation arising in the construction of quadratic cost functionals, i.e. Lyapunov functionals, for a linear time-delay system with a constant and a distributed delay is investigated. We present a…
We present a systematic method to derive an ordinary differential equation for any Feynman integral, where the differentiation is with respect to an external variable. The resulting differential equation is of Fuchsian type. The method can…
In this paper, the fractional projective Riccati expansion method is proposed to solve fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional Burgers equation, the space-time…
The Hermite-Birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered. Each proposed interpolant is expressed as a linear combination of basis functions, the…
We present a novel extension of the SINDy framework to delay differential equations with {\it distributed delays} and {\it renewal equations}, where typically the dependence from the past manifests via integrals in which the history is…
This paper is in continuation of the authors' recently published paper (Journal of Mathematical Physics 55(2014)083519) in which computational solutions of an unified reaction-diffusion equation of distributed order associated with Caputo…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
The paper is an inquiry of the algebraic foundations of the theory of dispersionless integrable hierarchies, like the dispersionless KP and modified KP hierarchies and the universal Whitham's hierarchy of genus zero. It stands out for the…
We study the integrable structure of the Dirichlet boundary problem in two dimensions and extend the approach to the case of planar multiply-connected domains. The solution to the Dirichlet boundary problem in multiply-connected case is…