Results 31 to 40 of about 36,805 (178)
Solutions of the Perturbed KDV Equation for Convecting Fluids by Factorizations
, 2009 In this paper, we obtain some new explicit travelling wave solutions of the perturbed KdV equation through recent factorization techniques that can be performed when the coefficients of the equation fulfill a certain condition. The solutions are obtained
Cornejo-Perez, O., Rosu, H. C.
core +1 more source
Periodic solutions of Abel differential equations
Journal of Mathematical Analysis and Applications, 2007 For a class of polynomial non-autonomous differential equations of degree n, we use phase plane analysis to show that each equation in this class has n periodic solutions. The result implies that certain rigid two-dimensional systems have at most one limit cycle which appears through multiple Hopf bifurcation.
openaire +2 more sources
U(1)-invariant membranes: the geometric formulation, Abel and pendulum differential equations
, 2010 The geometric approach to study the dynamics of U(1)-invariant membranes is developed. The approach reveals an important role of the Abel nonlinear differential equation of the first type with variable coefficients depending on time and one of the ...
A. A. Zheltukhin +11 more
core +1 more source
Nonlocal symmetries of Riccati and Abel chains and their similarity reductions
, 2012 We study nonlocal symmetries and their similarity reductions of Riccati and Abel chains. Our results show that all the equations in Riccati chain share the same form of nonlocal symmetry.
Bluman G. W. +5 more
core +1 more source
On Expansion of a Solution of General Non-autonomous Polynomial Differential Equation [PDF]
, 2014 We give a recursive formula for an expansion of a solution of a general non-autonomous polynomial differential equation. The formula is given on the algebraic level with a use of shuffle product. This approach minimizes the number of integrations on each
Pietrzkowski, Gabriel
core +2 more sources
Integrable Abel equations and Vein's Abel equation [PDF]
, 2016 We first reformulate and expand with several novel findings some of the basic results in the integrability of Abel equations. Next, these results are applied to Vein's Abel equation whose solutions are expressed in terms of the third order hyperbolic ...
Mancas, Stefan C., Rosu, Haret C
core +3 more sources
Abel-like differential equations with a unique limit cycle [PDF]
Nonlinear Analysis: Theory, Methods & Applications, 2011 Agraïments: M.J.A. was partially supported by grants MTM2005-06098-C02-1. J.L.B. and M.F. were partially supported by grant FEDER(UE) MTM2008-05460.
Álvarez Torres, María Jesús +2 more
openaire +5 more sources
Five-dimensional monopole equation with hedgehog ansatz and Abel’s differential equation [PDF]
Physical Review D, 2008 We review the generalized monopole in the five-dimensional Euclidean space. A numerical solution with the Hedge-Hog ansatz is studied. The Bogomol'nyi equation becomes a second order autonomous non-linear differential equation. The equation can be translated into the Abel's differential equation of the second kind and is an algebraic differential ...
openaire +2 more sources
On the Abel differential equations of third kind
Discrete & Continuous Dynamical Systems - B, 2020 In this paper, using Poincaré compactification, the authors give a classification of the topological phase portraits of a special kind of quadratic differential systems, namely the Abel quadratic equation of third kind. The paper also describes the maximal number of polynomial solutions that Abel polynomial differential equations can have.
Oliveira, Regilene, Valls, Cláudia
openaire +3 more sources
Advances in Difference Equations, 2021 In this paper, we extend existing population growth models and propose a model based on a nonlinear cubic differential equation that reveals itself as a special subclass of Abel differential equations of first kind.
Benjamin Wacker, Jan Christian Schlüter
doaj +1 more source