Related papers: Partially integrable nonlinear equations with one …
We study a class of evolutionary partial differential systems with two components related to second order (in time) non-evolutionary equations of odd order in spatial variable. We develop the formal diagonalisation method in symbolic…
In this paper we present a system of two nonlinear partial differential equations of the second order, depending on the time and one spatial coordinate. It can be written as a system of two Burgers equations, which allows one to immediately…
In this paper are examined general classes of linear and non-linear analytical systems of partial differential equations. Indeed the integrability conditions are found and if they are satisfied, the solutions are given as functional series…
In this paper, we consider a class of singular nonlinear first order partial differential equations $t(\partial u/\partial t)=F(t,x,u, \partial u/\partial x)$ with $(t,x) \in \mathbb{R} \times \mathbb{C}$ under the assumption that…
We consider a family of higher-order Boussinesq equations with an arbitrary nonlinearity. We determine the classes of equations so that a certain type of Lie symmetry algebra is admitted in this family. In case of a quadratic nonlinearity…
The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…
We study partial differential equations of second order (in time) that possess a hierarchy of infinitely many higher symmetries. The famous Boussinesq equation is a member of this class after the extension of the differential polynomial…
In this work we study the solutions to some fractional higher-order equations. Special cases in which time-fractional derivatives take integer values are also examined and the explicit solutions are presented. Such solutions can be…
In this paper we show that an arbitrary solution of one ordinary difference equation is also a solution for a hierarchy of integrable difference equations. We also provide an example of such a solution that is related to sequence generated…
The paper represents the method for construction of the families of particular solutions to some new classes of $(n+1)$ dimensional nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic…
In this paper we discuss the first order partial differential equations resolved with any derivatives. At first, we transform the first order partial differential equation resolved with respect to a time derivative into a system of linear…
In this paper, we consider a nonlinear Fuchsian type partial differential equation of the second order in the complex domain. Under a very weak assumption, we show the uniqueness of the solution. The result is applied to the problem of…
We investigate existence of solitonic solutions for higher-order partial differential equations with polynomial nonlinearities. Using the Hirota method we obtain classification for higher-order integrable systems of equations.
The problem of classification into symmetry integrable classes is solved for a family of second order nonlinear evolution equations labeled by arbitrary functions. Four nonequivalent symmetry integrable classes are thus obtained and the…
Motivated by the study of systems of higher order boundary value problems with functional boundary conditions, we discuss, by topological methods, the solvability of a fairly general class of systems of perturbed Hammerstein integral…
A series of systems of nonlinear equations with affine Weyl group symmetry of type $A^{(1)}_l$ is studied. This series gives a generalization of Painlev\'e equations $P_{IV}$ and $P_{V}$ to higher orders.
We show how to reduce the problem of solving members of a certain family of nonlinear differential equations to that of solving some corresponding linear differential equations.
We present here the explicit parametric solutions of second order differential equations invariant under time translation and rescaling and third order differential equations invariant under time translation and the two homogeneity…
A class of two-dimensional systems of second-order ordinary differential equations is identified in which a system requires fewer Lie point symmetries than required to solve it. The procedure distinguishes among those which are…
In this article, we discuss sixth-order and seventh-order iterative methods for nonlinear equations. Derivative-based and derivative-free, both categories are presented for said iterative methods. Especially sixth-order derivative-based and…