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Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2016, Volume 435, Issue 1, pp. 735 - 745
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2013, Volume 400, Issue 2, pp. 624 - 634
This paper investigates the integrability of a generalized (2+1)-dimensional Korteweg–de Vries equation. With the aid of binary Bell polynomials, its bilinear... 
Darboux covariant Lax pair | Binary Bell polynomial | [formula omitted]-soliton solution | Infinite conservation law | Lax pair | Bäcklund transformation | N-soliton solution | MATHEMATICS, APPLIED | KP HIERARCHY | MATHEMATICS | WAVES | KDV EQUATION | Backlund transformation | CONSERVATION-LAWS | N-SOLITON SOLUTIONS | COMBINATORICS | TRANSFORMATIONS
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 02/2012, Volume 45, Issue 5, pp. 055203 - 29
Journal Article
Modern Physics Letters B, ISSN 0217-9849, 05/2015, Volume 29, Issue 12, p. 1550051
Journal Article
Journal of Dynamics and Differential Equations, ISSN 1040-7294, 06/2017, Volume 29, Issue 2, pp. 597 - 613
In this paper we study the local integrability and linearizability of quadratic three dimensional systems of the form (x) over dot = x + a(12)xy + a(13)xz +... 
Three dimensional system | Linearizability | Quadratic systems | Resonant center | Decomposition of affine varieties | First integral | MATHEMATICS, APPLIED | VECTOR-FIELDS | EMBEDDING FLOWS | LOTKA-VOLTERRA SYSTEMS | POLYNOMIAL DIFFERENTIAL-SYSTEMS | MATHEMATICS | POINTS | DARBOUX INTEGRABILITY | ANALYTIC NORMALIZATION
Journal Article
Acta Mathematica Sinica, English Series, ISSN 1439-8516, 6/2018, Volume 34, Issue 6, pp. 947 - 958
Journal Article
Studies in Applied Mathematics, ISSN 0022-2526, 04/2014, Volume 132, Issue 3, pp. 212 - 246
With the inhomogeneities of media taken into account, under investigation is hereby a generalized variable‐coefficient forced Korteweg‐de Vries (vc‐fKdV)... 
SYSTEM | BINARY DARBOUX TRANSFORMATION | MATHEMATICS, APPLIED | NONLINEAR EQUATIONS | SOLITARY WAVES | KDV EQUATION | MODEL | KADOMTSEV-PETVIASHVILI EQUATION | PERIODIC-WAVE SOLUTIONS | RATIONAL CHARACTERISTICS
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 01/2016, Volume 368, Issue 1, pp. 607 - 620
Liouvillian first integrals of differential equations, Trans. Amer. Math. Soc. 333 (1992), 673-688) proved the equivalence between Liouvillian integrability... 
Darboux integrability | Galois group | Liouville integrability | Jacobian multiplier | INTEGRALS | MATHEMATICS | DARBOUX THEORY
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 01/2017, Volume 42, pp. 699 - 708
•An integrable nonlocal modified Korteweg-de Vries equation (mKdV) is proposed.•Darboux transformation for the nonlocal mKdV equation is constructed.•Exact... 
Soliton solutions | Integrability | Nonlocal modified Korteweg-de Vries equation | Darboux transformation | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PLASMA | SYMMETRY | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL
Journal Article
Nonlinear Dynamics, ISSN 0924-090X, 9/2014, Volume 77, Issue 4, pp. 1441 - 1453
Journal Article
International Journal of Non-Linear Mechanics, ISSN 0020-7462, 03/2015, Volume 69, pp. 129 - 136
We study the Darboux integrability of the Moon–Rand polynomial differential system. Moreover we study the limit cycles of the perturbed Moon–Rand system... 
Exponential factors | Limit cycles | Darboux polynomials | Darboux first integrals | Averaging theory | MECHANICS | DIFFERENTIAL-SYSTEMS | Origins | Bifurcations | Nonlinearity | Polynomials | Perturbation
Journal Article
Physica Scripta, ISSN 0031-8949, 03/2014, Volume 89, Issue 3, pp. 38003 - 9
Journal Article
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 06/2020, Volume 53, p. 103051
We study a Chemostat system of the form ẋ=−qx+R̃K+yxy,ẏ=(c̃−y)q−R̃ã(K+y)xy,where q>0, R̃>0, K>0, c̃>0 and ã≠0. This system appears in competition modelling... 
Chemostat systems | Invariant algebraic curves | Darboux polynomials | Liouvillian first integrals | Phase portraits | Puiseux series | MATHEMATICS, APPLIED | 1ST INTEGRALS | MODEL
Journal Article
Nonlinear Dynamics, ISSN 0924-090X, 2015, Volume 80, Issue 1-2, pp. 353 - 361
The first objective of this paper was to study the Darboux integrability of the polynomial differential system (x) over dot = y, (y) over dot = z, (z) over dot... 
Zero-Hopf bifurcation | Darboux integrability | Averaging theory | MECHANICS | CURVES | ENGINEERING, MECHANICAL | Economic models | Bifurcations | Polynomials | Hopf bifurcation | Nonlinear dynamics | Origins | Amplitudes | Nonlinearity | Mathematical models | Dynamical systems
Journal Article
Physics Letters A, ISSN 0375-9601, 2008, Volume 372, Issue 7, pp. 1009 - 1017
An n-dimensional solution family of the Jacobi equations is characterized and investigated, including the global determination of its main features: the... 
Casimir invariants | Jacobi identities | Finite-dimensional Poisson systems | Darboux' theorem | PDEs | PHYSICS, MULTIDISCIPLINARY | DYNAMICAL-SYSTEMS | CLASSIFICATION | LOTKA-VOLTERRA EQUATIONS | HAMILTONIAN-STRUCTURE | finite-dimensional Poisson systems
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 07/2017, Volume 50, Issue 34, pp. 1 - 26
In this paper we prove that the trapezoidal H-4 and the H-6 families of quadequations are Darboux integrable by constructing their first integrals. This result... 
general solutions | integrable discrete equations | Darboux integrability | CAC | linearizable discrete equations | QUAD-EQUATIONS | SYMMETRIES | PHYSICS, MULTIDISCIPLINARY | DIFFERENCE-EQUATIONS | CLASSIFICATION | PHYSICS, MATHEMATICAL | CONSISTENT | DISCRETE | LAX PAIRS
Journal Article
CHAOS SOLITONS & FRACTALS, ISSN 0960-0779, 01/2016, Volume 82, pp. 131 - 138
We study the Darboux integrability of a differential system in R5 with parameters coming from a chemical reaction model. In particular, we find all its Darboux... 
GRAPH | MASS-ACTION KINETICS | PHYSICS, MULTIDISCIPLINARY | INJECTIVITY | Exponential factor | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Darboux integrability | Darboux polynomial | SYSTEMS | CHEMICAL-REACTION NETWORKS | Chemical reaction network | MULTIPLE EQUILIBRIA
Journal Article
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