Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2016, Volume 435, Issue 1, pp. 735 - 745

A (1+1)-dimensional nonlinear evolution equation with Lax integrability is investigated in this paper with the aid of differential forms and exterior...

[formula omitted]-Dimensional nonlinear evolution equation with Lax integrability | Exterior differential | Frobenius theorem | Complete integrability | Darboux transformation | (1+1)-Dimensional nonlinear evolution equation with Lax integrability | SYSTEM | MATHEMATICS, APPLIED | PROLONGATION STRUCTURES | WAVE SOLUTIONS | ROGUE WAVES | MATHEMATICS | SOLITON-SOLUTIONS | OPTICAL-FIBER | CONSERVATION-LAWS | WATER

[formula omitted]-Dimensional nonlinear evolution equation with Lax integrability | Exterior differential | Frobenius theorem | Complete integrability | Darboux transformation | (1+1)-Dimensional nonlinear evolution equation with Lax integrability | SYSTEM | MATHEMATICS, APPLIED | PROLONGATION STRUCTURES | WAVE SOLUTIONS | ROGUE WAVES | MATHEMATICS | SOLITON-SOLUTIONS | OPTICAL-FIBER | CONSERVATION-LAWS | WATER

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 02/2019, Volume 77, Issue 3, pp. 770 - 778

We consider the Heisenberg ferromagnetic spin chain equation, which is governed by the (2+1)-dimensional nonlinear Schrödinger-type equation. Based on the...

Heisenberg ferromagnetic spin chain equation | Stability analysis | Hirota bilinear form | Lax pair | Bäcklund transformation | Darboux transformation | MATHEMATICS, APPLIED | SCHRODINGER-EQUATION | INFINITE CONSERVATION-LAWS | PERIODIC-WAVE SOLUTIONS | ROGUE WAVES | BOUNDARY VALUE-PROBLEMS | DYNAMICS | Backlund transformation | HOMOCLINIC BREATHER WAVES | Conservation laws | Stability | Chain dynamics | Integral equations | Modulation | Chains | Transformations | Schroedinger equation | Ferromagnetism

Heisenberg ferromagnetic spin chain equation | Stability analysis | Hirota bilinear form | Lax pair | Bäcklund transformation | Darboux transformation | MATHEMATICS, APPLIED | SCHRODINGER-EQUATION | INFINITE CONSERVATION-LAWS | PERIODIC-WAVE SOLUTIONS | ROGUE WAVES | BOUNDARY VALUE-PROBLEMS | DYNAMICS | Backlund transformation | HOMOCLINIC BREATHER WAVES | Conservation laws | Stability | Chain dynamics | Integral equations | Modulation | Chains | Transformations | Schroedinger equation | Ferromagnetism

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

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

Nonlinear Dynamics, ISSN 0924-090X, 2/2018, Volume 91, Issue 3, pp. 1909 - 1920

The integrability of the reverse space–time nonlocal Sasa–Satsuma equation in the Liouville sense is established by showing the existence of infinitely many...

Engineering | Vibration, Dynamical Systems, Control | Nonlinear waves | Integrability | Gauge equivalent | Classical Mechanics | Automotive Engineering | Mechanical Engineering | Reverse space–time nonlocal Sasa–Satsuma equation | FIBERS | DARBOUX TRANSFORMATION | MECHANICS | SOLITON-SOLUTIONS | MODULATION INSTABILITY | DYNAMICS | DARK | Reverse space-time nonlocal Sasa-Satsuma equation | ENGINEERING, MECHANICAL | Yuan (China) | Environmental law | Business schools | Conservation laws | Defocusing | Equivalence | Integral equations

Engineering | Vibration, Dynamical Systems, Control | Nonlinear waves | Integrability | Gauge equivalent | Classical Mechanics | Automotive Engineering | Mechanical Engineering | Reverse space–time nonlocal Sasa–Satsuma equation | FIBERS | DARBOUX TRANSFORMATION | MECHANICS | SOLITON-SOLUTIONS | MODULATION INSTABILITY | DYNAMICS | DARK | Reverse space-time nonlocal Sasa-Satsuma equation | ENGINEERING, MECHANICAL | Yuan (China) | Environmental law | Business schools | Conservation laws | Defocusing | Equivalence | Integral equations

Journal Article

5.
Full Text
On the integrability of a generalized variable-coefficient Kadomtsev–Petviashvili equation

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8121, 02/2012, Volume 45, Issue 5, pp. 055203 - 29

By considering the inhomogeneities of media, a generalized variable-coefficient Kadomtsev-Petviashvili (vc-KP) equation is investigated, which can be used to...

SOLITON-LIKE SOLUTIONS | BINARY DARBOUX TRANSFORMATION | WATER-WAVES | BACKLUND-TRANSFORMATIONS | NONLINEAR EQUATIONS | PHYSICS, MULTIDISCIPLINARY | LAX PAIR | SYMBOLIC COMPUTATION | KDV EQUATION | PAINLEVE PROPERTY | PHYSICS, MATHEMATICAL | PERIODIC-WAVE SOLUTIONS | Inhomogeneities | Asymptotic properties | Mathematical analysis | Solitons | Transformations | Integral calculus | Formalism | Density | Constraining

SOLITON-LIKE SOLUTIONS | BINARY DARBOUX TRANSFORMATION | WATER-WAVES | BACKLUND-TRANSFORMATIONS | NONLINEAR EQUATIONS | PHYSICS, MULTIDISCIPLINARY | LAX PAIR | SYMBOLIC COMPUTATION | KDV EQUATION | PAINLEVE PROPERTY | PHYSICS, MATHEMATICAL | PERIODIC-WAVE SOLUTIONS | Inhomogeneities | Asymptotic properties | Mathematical analysis | Solitons | Transformations | Integral calculus | Formalism | Density | Constraining

Journal Article

Modern Physics Letters B, ISSN 0217-9849, 05/2015, Volume 29, Issue 12, p. 1550051

In this paper, a (3+1)-dimensional generalized variable-coefficients Kadomtsev–Petviashvili (gvcKP) equation is proposed, which describes many nonlinear...

Bell polynomial | Infinite conservation law | Hirota bilinear form | Lax pair | Solitary wave solution | Bäcklund transformation | PHYSICS, CONDENSED MATTER | DARBOUX TRANSFORMATION | PHYSICS, APPLIED | PHYSICS, MATHEMATICAL | PERIODIC-WAVE SOLUTIONS | infinite conservation law | solitary wave solution | EVOLUTION | BOUSSINESQ | EXPANSION | Backlund transformation | LATTICE

Bell polynomial | Infinite conservation law | Hirota bilinear form | Lax pair | Solitary wave solution | Bäcklund transformation | PHYSICS, CONDENSED MATTER | DARBOUX TRANSFORMATION | PHYSICS, APPLIED | PHYSICS, MATHEMATICAL | PERIODIC-WAVE SOLUTIONS | infinite conservation law | solitary wave solution | EVOLUTION | BOUSSINESQ | EXPANSION | Backlund transformation | LATTICE

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

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

We study the Hindmarsh–Rose burster which can be described by the differential system $$\dot x = y - {x^3} + b{x^2} + I - z,\dot y = 1 - 5{x^2} - y,\dot z =...

34C05 | 34C14 | rational integrability | Darboux polynomials | invariant algebraic surfaces | exponential factors | 34A34 | Darboux first integrals | Polynomial integrability | Mathematics, general | Mathematics | Hindmarsh–Rose burster | Hindmarsh-Rose burster | MATHEMATICS, APPLIED | MULTIPLICITY | 1ST INTEGRALS | DIFFERENTIAL-EQUATIONS | VECTOR-FIELDS | NEURON MODEL | MATHEMATICS | SYNCHRONIZATION | SYSTEMS | OSCILLATIONS | Dynamic tests | Algebra | Mathematical analysis | Invariants

34C05 | 34C14 | rational integrability | Darboux polynomials | invariant algebraic surfaces | exponential factors | 34A34 | Darboux first integrals | Polynomial integrability | Mathematics, general | Mathematics | Hindmarsh–Rose burster | Hindmarsh-Rose burster | MATHEMATICS, APPLIED | MULTIPLICITY | 1ST INTEGRALS | DIFFERENTIAL-EQUATIONS | VECTOR-FIELDS | NEURON MODEL | MATHEMATICS | SYNCHRONIZATION | SYSTEMS | OSCILLATIONS | Dynamic tests | Algebra | Mathematical analysis | Invariants

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

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

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

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

We study the Darboux and the analytic integrability of the Rucklidge system.

Engineering | Vibration, Dynamical Systems, Control | Analytic first integrals | Darboux polynomials | Darboux first integrals | Mechanics | Automotive Engineering | Exponential factors | Mechanical Engineering | MECHANICS | DIFFERENTIAL-SYSTEMS | ENGINEERING, MECHANICAL

Engineering | Vibration, Dynamical Systems, Control | Analytic first integrals | Darboux polynomials | Darboux first integrals | Mechanics | Automotive Engineering | Exponential factors | Mechanical Engineering | MECHANICS | DIFFERENTIAL-SYSTEMS | ENGINEERING, MECHANICAL

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

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

We discuss how point transformations can be used for the study of integrability, in particular, for deriving classes of integrable variable-coefficient...

equivalence transformations | variable coefficient integrable equations | Lax pairs | fifth-order KdV equations | admissible transformations | BACKLUND-DARBOUX TRANSFORMATION | VARYING SOLITARY WAVES | PHYSICS, MULTIDISCIPLINARY | DE-VRIES EQUATION | EVOLUTION-EQUATIONS | KORTEWEG-DEVRIES | Evolution | Transformations | Equivalence | Mathematical analysis | Differential equations

equivalence transformations | variable coefficient integrable equations | Lax pairs | fifth-order KdV equations | admissible transformations | BACKLUND-DARBOUX TRANSFORMATION | VARYING SOLITARY WAVES | PHYSICS, MULTIDISCIPLINARY | DE-VRIES EQUATION | EVOLUTION-EQUATIONS | KORTEWEG-DEVRIES | Evolution | Transformations | Equivalence | Mathematical analysis | Differential equations

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

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

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

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

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

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

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 03/2017, Volume 50, Issue 16, p. 165202

In this paper we study certain integrability properties of the supersymmetric sine-Gordon equation. We construct Lax pairs with their zero-curvature...

supersymmetric version of the SymTafel immersion formula | solitonic surfaces | supersymmetric versions of the Bcklund and Darboux transformations | supersymmetric extension of the sine-Gordon equation | Gordon equation | INVARIANCE | DARBOUX TRANSFORMATION | PHYSICS, MULTIDISCIPLINARY | supersymmetric version of the Sym-Tafel immersion formula | PHYSICS, MATHEMATICAL | supersymmetric extension of the sine | supersymmetric versions of the Backlund and Darboux transformations | MECHANICS | MODELS | CONSERVATION-LAWS | KORTEWEG-DEVRIES

supersymmetric version of the SymTafel immersion formula | solitonic surfaces | supersymmetric versions of the Bcklund and Darboux transformations | supersymmetric extension of the sine-Gordon equation | Gordon equation | INVARIANCE | DARBOUX TRANSFORMATION | PHYSICS, MULTIDISCIPLINARY | supersymmetric version of the Sym-Tafel immersion formula | PHYSICS, MATHEMATICAL | supersymmetric extension of the sine | supersymmetric versions of the Backlund and Darboux transformations | MECHANICS | MODELS | CONSERVATION-LAWS | KORTEWEG-DEVRIES

Journal Article

No results were found for your search.

Cannot display more than 1000 results, please narrow the terms of your search.