Related papers: Generalizations of the short pulse equation
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
An extension of the ideas of the Prelle-Singer procedure to second order differential equations is proposed. As in the original PS procedure, this version of our method deals with differential equations of the form…
We classify solutions of finite Morse index of the fractional Lane- Emden equation
The solvability in $W^{2}_{p}(\bR^{d})$ spaces is proved for second-order elliptic equations with coefficients which are measurable in one direction and VMO in the orthogonal directions in each small ball with the direction depending on the…
We prove lower bounds on the error incurred when approximating any oscillating function using piecewise polynomial spaces. The estimates are explicit in the polynomial degree and have optimal dependence on the meshwidth and frequency when…
We study the short pulse dynamics in the deterministic and stochastic environment in this thesis. The integrable short pulse equation is a modelling equation for ultra-short pulse propagation in the infrared range in the optical fibers. We…
We give an exceptionally short derivation of Schroedinger's equation by replacing the idealization of a point particle by a density distribution.
New exact solutions for the heat equation with a polynomial non-linearity and for the Fisher equation are found. An extended class of non-linear heat equations admitting solitary wave solutions is found. The generalization of the Fisher…
In this paper, we consider central complete and incomplete Bell polynomials which are generalizations of the recently introduced central Bell polynomials and central analogues for the complete and incomplete Bell polynomials. We investigate…
Given a weight of sl(n), we derive a system of variable-coefficient second-order linear partial differential equations that determines the singular vectors in the corresponding Verma module. Moreover, we completely solve the system in a…
Second-order variational type equations for spatial point processes are established. In case of log linear parametric models for pair correlation functions, it is demonstrated that the variational equations can be applied to construct…
We consider the fractional generalizations of Liouville equation. The normalization condition, phase volume, and average values are generalized for fractional case.The interpretation of fractional analog of phase space as a space with…
We demonstrate how to separate the rotational degrees of freedom in a quantum N-body problem completely from the internal ones. It is shown that any common eigenfunction of the total orbital angular momentum ($\ell$) and the parity in the…
A quaternionic partial differential equation is shown to be a generalisation of the Riccati ordinary differential equation and its relationship with the Schrodinger equation is established. Various approaches to the problem of finding…
We describe a way of solving a partial differential equation using the differential invariants of its point symmetries. By first solving its quotient PDE, which is given by the differential syzygies in the algebra of differential…
By imposing special compatible similarity constraints on a class of integrable partial $q$-difference equations of KdV-type we derive a hierarchy of second-degree ordinary $q$-difference equations. The lowest (non-trivial) member of this…
The concept of moment differentiation is extended to the class of moment summable functions, giving rise to moment differential properties. The main result leans on accurate upper estimates for the integral representation of the moment…
This paper concerns local gradient estimates to solutions of general conformally invariant fully nonlinear elliptic equations of second order.
Extencion of Krein's special method for solving of integral equation to that method for solving of systems of integral equations is established. Generalizations of formulae for solution of integral equations are obtained. The result…
In this paper we established the condition for a curve to satisfy stochastic generalized fractional HP (Hamilton-Pontryagin) equations. These equations are described using Ito integral. We have also considered the case of stochastic…