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Integrability of Lie Systems Through Riccati Equations
Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyze a geometric method to construct...
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Positive periodic solution for a nonautonomous periodic model of population with time delays and impulses
In this paper, a nonautonomous periodic model of population with time delays and impulses, which arises in order to describe the control of a single...
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Exact traveling wave solutions and bifurcations in a nonlinear elastic rod equation
The exact parametric representations of the traveling wave solutions for a nonlinear elastic rod equation are considered. By using the method of...
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Semiseparable Integral Operators and Explicit Solution of an Inverse Problem for a Skew-Self-Adjoint Dirac-Type System
Inverse problem to recover the skew-self-adjoint Dirac-type system from the generalized Weyl matrix function is treated in the paper. Sufficient...
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Popular ansatz methods and solitary wave solutions of the Kuramoto-Sivashinsky equation
Some methods to look for exact solutions of nonlinear differential equations are discussed. It is shown that many popular methods are equivalent to...
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A Novel Riccati Sequence
Hierarchies of evolution partial differential equations have become well-established in the literature over the last thirty years. More recently...
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The lie group and integrability of the Fisher type travelling wave equation
For the Fisher-type wave equation, which has two stable states and one unstable state, it is proved that only in two particular cases, the...
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Solvable systems of linear differential equations
The asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential...
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Stochastische Differentialgleichungen für Finanzmarktmodelle
In this contribution we investigate the role of ordinary and stochastic differential equations for modeling capital markets. In particular, we look...
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Symmetry Approaches for Reductions of PDEs, Differential Constraints and Lagrange-Charpit Method
Many methods for reducing and simplifying differential equations are known. They provide various generalizations of the original symmetry approach of...
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Explicit solution for Lamé and other PDE systems
We provide a general series form solution for second-order linear PDE system with constant coefficients and prove a convergence theorem. The...
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Solving the chemical master equation for monomolecular reaction systems analytically
The stochastic dynamics of a well-stirred mixture of molecular species interacting through different biochemical reactions can be accurately modelled...
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Reducible Ordinary Differential Equations
The class of reducible differential equations under consideration here includes the class of symmetric systems, and examples show that the inclusion...
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Computation of All Polynomial Solutions of a Class of Nonlinear Differential Equations
A class of nonlinear differential equations is considered. We show that all their polynomial solutions can be computed in a systematic manner....
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The Center Problem for a Linear Center Perturbed by Homogeneous Polynomials
The centers of the polynomial differential systems with a linear center perturbed by homogeneous polynomials have been studied for the degrees s = 2,...
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Constructing and solving equations – inverse operations
Two inverse operations are considered in this paper: solving a given equation, i.e. finding its solution space, and constructing an equation from a...
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Characterization of the Newtonian Free Particle System in \(m\geqslant 2\) Dependent Variables
We treat the problem of linearizability of a system of second order ordinary differential equations. The criterion we provide has applications to...
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On a method to transform algebraic differential equations into universal equations
The paper introduces an algorithm which transforms homogeneous algebraic differential equations into universal differential equations (in the sense...