Related papers: Nonlinear differential equations with exact soluti…
A non-linear differential equation arising from a stochastic process known as branching Brownian motion is considered. We find an explicit solution and show the uniqueness of the solution under some boundedness conditions using…
In classical continuum physics, a wave is a mechanical disturbance. Whether the disturbance is stationary or traveling and whether it is caused by the motion of atoms and molecules or the vibration of a lattice structure, a wave can be…
This paper is dedicated to present an exact solution for a nonlinear differential equation so-called Abel equation. This equation was known as one of the group of unsolvable differential equations. The present method is applicable for any…
A new method named rational expansion method of exponent function is presented to find exact traveling wave solutions of differential-difference equations. This method generalizes the so-called tanh-method and other similar methods. Some…
We propose a method for transformating linear and nonlinear hypersingular integral equations into ordinary differential equations. Linear and nonlinear polyhypersingular integral equations are transformed into partial differential…
The Riccati equation method is used to establish a new stability criteria for linear systems of ordinary differential equations. Two examples are presented in which the obtained result is compared with the results obtained by the Lyapunov…
Nonlinear filtering is a pivotal problem that has attracted significant attention from mathematicians, statisticians, engineers, and various other scientific disciplines. The solution to this problem is governed by the so-called filtering…
In this work, an efficient approximation scheme has been proposed for getting accurate approximate solution of nonlinear partial differential equations with constant or variable coefficients satisfying initial conditions in a series of…
A method to construct the exact solution of the PDE is presents, which combines the two kind methods(the nonlinear transformation and RQ(Reduction the PDE to a Quadrature problem) method).The nonlinear diffusion equation is chosen to…
Some properties of global solution of scalar Riccati equation are studied. On the basis of these properties using the Whiburn's and Leighton - Nehary's theorems some oscillatory and criteria are proved for second order linear systems of…
In this paper we consider a class of fourth order nonlinear integro-differential equations with Navier boundary conditions. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…
A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical…
Differential Equations are among the most important Mathematical tools used in creating models in the science, engineering, economics, mathematics, physics, aeronautics, astronomy, dynamics, biology, chemistry, medicine, environmental…
Ten new exact solutions of the Riccati equation $dy/dx=a(x)+b(x)y+c(x)y^{2}$ are presented. The solutions are obtained by assuming certain relations among the coefficients $a(x)$, $b(x)$ and $c(x)$ of the Riccati equation, in the form of…
We define a proper differential sequence of ordinary differential equations and introduce a method to derive an alternative sequence of integrals for such a sequence. We describe some general properties which are illustrated by several…
A theorem that constructs a path integral solution for general second order partial differential equations is specialized to obtain path integrals that are solutions of elliptic, parabolic, and hyperbolic linear second order partial…
Differential equations with constant and variable coefficients over octonions are investigated. It is found that different types of differential equations over octonions can be resolved. For this purpose non-commutative line integration is…
A theorem providing necessary conditions enabling one to map a nonlinear system of first order partial differential equations to an equivalent first order autonomous and homogeneous quasilinear system is given. The reduction to quasilinear…
We describe a set of Gaussian Process based approaches that can be used to solve non-linear Ordinary Differential Equations. We suggest an explicit probabilistic solver and two implicit methods, one analogous to Picard iteration and the…
The Riccati equation method is used to establish oscillation and non-oscillation criteria for second order linear nonhomogeneous functional-differential equations.We show that the obtained oscillation criterion is a generalization of J. S.…