Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 10/2016, Volume 31, pp. 388 - 408

Under investigation in this paper is a generalized (2+1)-dimensional Boussinesq equation, which can be used to describe the water wave interaction. By using...

The (2+1)-dimensional Boussinesq equation | Bell’s polynomials | Soliton solution | Periodic wave solution | Infinite conservation laws | Bäcklund transformation | Bell's polynomials | POLYNOMIALS | MATHEMATICS, APPLIED | CAMASSA-HOLM EQUATION | Backlund transformation | RATIONAL CHARACTERISTICS | Environmental law

The (2+1)-dimensional Boussinesq equation | Bell’s polynomials | Soliton solution | Periodic wave solution | Infinite conservation laws | Bäcklund transformation | Bell's polynomials | POLYNOMIALS | MATHEMATICS, APPLIED | CAMASSA-HOLM EQUATION | Backlund transformation | RATIONAL CHARACTERISTICS | Environmental law

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 2/2016, Volume 83, Issue 3, pp. 1199 - 1215

A generalized (3+1)-dimensional nonlinear wave is investigated, which describes many nonlinear phenomena in liquid containing gas bubbles. In this paper, a...

Engineering | Vibration, Dynamical Systems, Control | A generalized (3+1)-dimensional nonlinear wave equation | Soliton solution | Infinite conservation laws | Bäcklund transformation | Mechanics | Bell’s polynomials | Automotive Engineering | Mechanical Engineering | Periodic wave solution | SYSTEM | 1-SOLITON SOLUTION | MODEL | ENGINEERING, MECHANICAL | MECHANICS | EVOLUTION | SOLITONS | BILINEAR EQUATIONS | KDV EQUATION | Backlund transformation | RATIONAL CHARACTERISTICS | Bell's polynomials | Environmental law | Conservation laws | Bubbles | Nonlinear phenomena | Transformations (mathematics) | Integral equations | Wave equations | Polynomials | Fluxes | Solitary waves

Engineering | Vibration, Dynamical Systems, Control | A generalized (3+1)-dimensional nonlinear wave equation | Soliton solution | Infinite conservation laws | Bäcklund transformation | Mechanics | Bell’s polynomials | Automotive Engineering | Mechanical Engineering | Periodic wave solution | SYSTEM | 1-SOLITON SOLUTION | MODEL | ENGINEERING, MECHANICAL | MECHANICS | EVOLUTION | SOLITONS | BILINEAR EQUATIONS | KDV EQUATION | Backlund transformation | RATIONAL CHARACTERISTICS | Bell's polynomials | Environmental law | Conservation laws | Bubbles | Nonlinear phenomena | Transformations (mathematics) | Integral equations | Wave equations | Polynomials | Fluxes | Solitary waves

Journal Article

Reports on Mathematical Physics, ISSN 0034-4877, 03/2019, Volume 83, Issue 1, pp. 21 - 48

The concept of sub-symmetry of a differential system was introduced in [40], where it was shown that a sub-symmetry is a considerably more powerful tool than a...

infinite conservation laws | Maxwell's equations | Euler equations | symmetry properties | non-Lagrangian systems | INVARIANT SOLUTIONS | PHYSICS, MATHEMATICAL | INFINITE SYMMETRIES | EULER | NOETHER THEOREM | Fluid dynamics | Laws, regulations and rules | Environmental law

infinite conservation laws | Maxwell's equations | Euler equations | symmetry properties | non-Lagrangian systems | INVARIANT SOLUTIONS | PHYSICS, MATHEMATICAL | INFINITE SYMMETRIES | EULER | NOETHER THEOREM | Fluid dynamics | Laws, regulations and rules | Environmental law

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 08/2016, Volume 37, pp. 362 - 373

•The conditionally Painleve integrable Jimbo–Miwa equation is investigated for multi-soliton solutions.•Bell-polynomials are used to obtain Backlund...

Lax system | Jimbo–Miwa equation | Bäcklund transformations | Bell polynomials | Infinite conservation laws | Extended three wave method | Jimbo-Miwa equation | MATHEMATICS, APPLIED | INTEGRABILITY | PHYSICS, FLUIDS & PLASMAS | DE-VRIES EQUATION | PHYSICS, MATHEMATICAL | Backlund transformations | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SOLITON-SOLUTIONS | COMBINATORICS | Environmental law

Lax system | Jimbo–Miwa equation | Bäcklund transformations | Bell polynomials | Infinite conservation laws | Extended three wave method | Jimbo-Miwa equation | MATHEMATICS, APPLIED | INTEGRABILITY | PHYSICS, FLUIDS & PLASMAS | DE-VRIES EQUATION | PHYSICS, MATHEMATICAL | Backlund transformations | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SOLITON-SOLUTIONS | COMBINATORICS | Environmental law

Journal Article

Computers and Fluids, ISSN 0045-7930, 01/2014, Volume 89, pp. 153 - 156

•The bilinear form and Bäcklund transformation are obtained by the Bell polynomials.•A new Bäcklund transformation is derived by the bilinear Bäcklund...

Binary Bell polynomials | Bilinear Bäcklund transformation | Lax pair | Infinite conservation laws | PAINLEVE ANALYSIS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Bilinear Backlund transformation | KADOMTSEV-PETVIASHVILI EQUATION | SOLITON SOLUTIONS | COMBINATORICS | Environmental law | Conservation laws | Computational fluid dynamics | Wave equations | Fluid flow | Transformations | Polynomials | Shallow water | Combinatorial analysis

Binary Bell polynomials | Bilinear Bäcklund transformation | Lax pair | Infinite conservation laws | PAINLEVE ANALYSIS | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Bilinear Backlund transformation | KADOMTSEV-PETVIASHVILI EQUATION | SOLITON SOLUTIONS | COMBINATORICS | Environmental law | Conservation laws | Computational fluid dynamics | Wave equations | Fluid flow | Transformations | Polynomials | Shallow water | Combinatorial analysis

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2017, Volume 447, Issue 2, pp. 867 - 881

We consider the Euler equations of incompressible inviscid fluid dynamics. We discuss a variational formulation of the governing equations in Lagrangian...

Conservation laws | Lagrangian coordinates | Euler equations | Symmetries | Incompressible flows | Time-periodic solution | MATHEMATICS, APPLIED | FLUID-FLOW | FORMULATION | MATHEMATICS | NAVIER-STOKES EQUATIONS | SPATIAL DIMENSIONS | INFINITE SYMMETRIES | Fluid dynamics | Environmental law | Force and energy

Conservation laws | Lagrangian coordinates | Euler equations | Symmetries | Incompressible flows | Time-periodic solution | MATHEMATICS, APPLIED | FLUID-FLOW | FORMULATION | MATHEMATICS | NAVIER-STOKES EQUATIONS | SPATIAL DIMENSIONS | INFINITE SYMMETRIES | Fluid dynamics | Environmental law | Force and energy

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 02/2011, Volume 52, Issue 2, pp. 022901 - 022901-20

This paper is devoted to studying symmetries of certain kinds of k-cosymplectic Hamiltonian systems in first-order classical field theories. Thus, we introduce...

SYSTEMS | FORMALISM | MANIFOLDS | PHYSICS, MATHEMATICAL | Hamiltonian systems | Matemàtiques i estadística | Sistemes dinàmics | 37K Infinite-dimensional Hamiltonian systems | Àrees temàtiques de la UPC | Equacions diferencials i integrals | FIELD THEORIES | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | SYMMETRY | MATHEMATICAL OPERATORS | QUANTUM OPERATORS | CONSERVATION LAWS | HAMILTONIANS | INVARIANCE PRINCIPLES | QUANTUM FIELD THEORY

SYSTEMS | FORMALISM | MANIFOLDS | PHYSICS, MATHEMATICAL | Hamiltonian systems | Matemàtiques i estadística | Sistemes dinàmics | 37K Infinite-dimensional Hamiltonian systems | Àrees temàtiques de la UPC | Equacions diferencials i integrals | FIELD THEORIES | PHYSICS OF ELEMENTARY PARTICLES AND FIELDS | SYMMETRY | MATHEMATICAL OPERATORS | QUANTUM OPERATORS | CONSERVATION LAWS | HAMILTONIANS | INVARIANCE PRINCIPLES | QUANTUM FIELD THEORY

Journal Article

Journal de mathématiques pures et appliquées, ISSN 0021-7824, 04/2012, Volume 97, Issue 4, pp. 318 - 390

We introduce a class of action integrals defined over probability measure-valued path space. We show that extremal point of such action exits and satisfies a...

Mass transport | Viscosity solution in space of measures | Hamilton–Jacobi equation | Compressible Euler equations | Hamilton-Jacobi equation | Compressible euler equations | MATHEMATICS | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | UNBOUNDED LINEAR TERMS | INFINITE DIMENSIONS | Environmental law

Mass transport | Viscosity solution in space of measures | Hamilton–Jacobi equation | Compressible Euler equations | Hamilton-Jacobi equation | Compressible euler equations | MATHEMATICS | VISCOSITY SOLUTIONS | MATHEMATICS, APPLIED | UNBOUNDED LINEAR TERMS | INFINITE DIMENSIONS | Environmental law

Journal Article

Studies in Applied Mathematics, ISSN 0022-2526, 07/2017, Volume 139, Issue 1, pp. 7 - 59

A nonlocal nonlinear Schrödinger (NLS) equation was recently found by the authors and shown to be an integrable infinite dimensional Hamiltonian equation....

MATHEMATICS, APPLIED | EVOLUTION | SOLITONS | CONSERVATION-LAWS | INFINITE NUMBER | INVERSE SCATTERING TRANSFORM

MATHEMATICS, APPLIED | EVOLUTION | SOLITONS | CONSERVATION-LAWS | INFINITE NUMBER | INVERSE SCATTERING TRANSFORM

Journal Article

Physical Review D, ISSN 2470-0010, 03/2017, Volume 95, Issue 6

We prove the Lorentz invariance of the angular momentum conservation law and the helicity sum rule for relativistic composite systems in the light-front...

SPIN | ELECTRODYNAMICS | ASTRONOMY & ASTROPHYSICS | DYNAMICS | RULES | FRAME | SCATTERING | INFINITE-MOMENTUM | PHYSICS, PARTICLES & FIELDS

SPIN | ELECTRODYNAMICS | ASTRONOMY & ASTROPHYSICS | DYNAMICS | RULES | FRAME | SCATTERING | INFINITE-MOMENTUM | PHYSICS, PARTICLES & FIELDS

Journal Article

Zeitschrift für Naturforschung A, ISSN 0932-0784, 04/2010, Volume 65, Issue 4, pp. 291 - 300

Under investigation in this paper, with symbolic computation, is the Sasa-Satsuma (SS) equation which can describe the propagation of ultra short pulses in...

Lax Pair | Infinite Number of Conservation Laws | Soliton Interaction | One-Soliton Solution | Sasa-Satsuma Equation | B¨acklund Transformation | One-soliton solution | Soliton interaction | Sasa-Satsuma equation | Lax pair | Bäcklund transformation | Infinite number of conservation laws | INVERSE SCATTERING METHOD | PHYSICS, MULTIDISCIPLINARY | STABILITY | CHEMISTRY, PHYSICAL | SYMBOLIC-COMPUTATION | MODEL | NONLINEAR SCHRODINGER-EQUATION | PAINLEVE ANALYSIS | VARIABLE-COEFFICIENTS | COMPLETE-INTEGRABILITY | PULSE-PROPAGATION | Backlund Transformation | DUSTY PLASMA

Lax Pair | Infinite Number of Conservation Laws | Soliton Interaction | One-Soliton Solution | Sasa-Satsuma Equation | B¨acklund Transformation | One-soliton solution | Soliton interaction | Sasa-Satsuma equation | Lax pair | Bäcklund transformation | Infinite number of conservation laws | INVERSE SCATTERING METHOD | PHYSICS, MULTIDISCIPLINARY | STABILITY | CHEMISTRY, PHYSICAL | SYMBOLIC-COMPUTATION | MODEL | NONLINEAR SCHRODINGER-EQUATION | PAINLEVE ANALYSIS | VARIABLE-COEFFICIENTS | COMPLETE-INTEGRABILITY | PULSE-PROPAGATION | Backlund Transformation | DUSTY PLASMA

Journal Article

Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, 09/2009, Volume 2009, Issue 9, p. P09009

The existence of true scale-invariance in slowly driven models of self-organized criticality without a conservation law, such as forest-fires or earthquake...

Percolation problems (theory) | Phase transitions into absorbing states (theory) | Self-organized criticality (theory) | Sandpile models (theory) | self-organized criticality (theory) | BRANCHING-PROCESSES | percolation problems (theory) | phase transitions into absorbing states (theory) | PHASE-TRANSITIONS | sandpile models (theory) | ABELIAN SANDPILE | PHYSICS, MATHEMATICAL | FOREST-FIRE MODEL | TANG-WIESENFELD SANDPILE | MECHANICS | INFINITE NUMBERS | MEAN-FIELD THEORY | POWER LAWS | ABSORBING STATES | CRITICAL-BEHAVIOR | Physics - Statistical Mechanics

Percolation problems (theory) | Phase transitions into absorbing states (theory) | Self-organized criticality (theory) | Sandpile models (theory) | self-organized criticality (theory) | BRANCHING-PROCESSES | percolation problems (theory) | phase transitions into absorbing states (theory) | PHASE-TRANSITIONS | sandpile models (theory) | ABELIAN SANDPILE | PHYSICS, MATHEMATICAL | FOREST-FIRE MODEL | TANG-WIESENFELD SANDPILE | MECHANICS | INFINITE NUMBERS | MEAN-FIELD THEORY | POWER LAWS | ABSORBING STATES | CRITICAL-BEHAVIOR | Physics - Statistical Mechanics

Journal Article

中国物理B：英文版, ISSN 1674-1056, 2012, Volume 21, Issue 11, pp. 20 - 25

We construct a nonlinear integrable coupling of discrete soliton hierarchy, and establish the infinite conservation laws （CLs） for the nonlinear integrable...

非线性离散 | 层次结构 | 无穷守恒律 | 可积耦合系统 | 格子 | 晶格 | Volterra | CLS | nonlinear integrable coupling system | infinite conservation law | Volterra lattice hierarchy | LIE-ALGEBRAS | PHYSICS, MULTIDISCIPLINARY | HIERARCHY | Conservation laws | Construction | Hierarchies | Lattices | Solitons | Paper | Nonlinearity | Joining

非线性离散 | 层次结构 | 无穷守恒律 | 可积耦合系统 | 格子 | 晶格 | Volterra | CLS | nonlinear integrable coupling system | infinite conservation law | Volterra lattice hierarchy | LIE-ALGEBRAS | PHYSICS, MULTIDISCIPLINARY | HIERARCHY | Conservation laws | Construction | Hierarchies | Lattices | Solitons | Paper | Nonlinearity | Joining

Journal Article

THEORETICAL AND MATHEMATICAL PHYSICS, ISSN 0040-5779, 07/2009, Volume 160, Issue 1, pp. 1042 - 1049

We study Lagrangian systems of partial differential equations admitting infinite-dimensional symmetry algebras parameterized by arbitrary functions of...

infinite symmetry | DARBOUX | INTEGRABLE HYPERBOLIC-EQUATIONS | SYMMETRIES | DENSITIES | PHYSICS, MULTIDISCIPLINARY | BOUNDARY-CONDITIONS | conservation law | DIRECT CONSTRUCTION METHOD | PHYSICS, MATHEMATICAL | Environmental law

infinite symmetry | DARBOUX | INTEGRABLE HYPERBOLIC-EQUATIONS | SYMMETRIES | DENSITIES | PHYSICS, MULTIDISCIPLINARY | BOUNDARY-CONDITIONS | conservation law | DIRECT CONSTRUCTION METHOD | PHYSICS, MATHEMATICAL | Environmental law

Journal Article

Physics Letters A, ISSN 0375-9601, 01/2011, Volume 375, Issue 3, pp. 493 - 497

Binary Bell polynomials are extended to systematically construct bilinear formalism, bilinear Bäcklund transformations, Lax pairs and infinite conservation...

Binary Bell polynomial | Bilinear Bäcklund transformation | Infinite conservation law | Nonisospectral KdV equation | Lax pair | SOLITON-SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | Bilinear Backlund transformation | BACKLUND | EVOLUTION-EQUATIONS | WAVE SOLUTIONS | Environmental law | Conservation laws | Bells | Construction | Decoupling | Mathematical analysis | Austenitic stainless steels | Solid state physics | Transformations | Formalism

Binary Bell polynomial | Bilinear Bäcklund transformation | Infinite conservation law | Nonisospectral KdV equation | Lax pair | SOLITON-SOLUTIONS | PHYSICS, MULTIDISCIPLINARY | Bilinear Backlund transformation | BACKLUND | EVOLUTION-EQUATIONS | WAVE SOLUTIONS | Environmental law | Conservation laws | Bells | Construction | Decoupling | Mathematical analysis | Austenitic stainless steels | Solid state physics | Transformations | Formalism

Journal Article

European Physical Journal Plus, ISSN 2190-5444, 06/2017, Volume 132, Issue 6

Under investigation in this paper is a generalized (3+1)-dimensional varible-coefficient nonlinear-wave equation, which has been presented for nonlinear waves...

INTERNAL SOLITARY WAVES | PHYSICS, MULTIDISCIPLINARY | SCHRODINGER-EQUATION | LIE SYMMETRIES | DYNAMICS | INFINITE CONSERVATION-LAWS | SYSTEMS | RATIONAL CHARACTERISTICS | BACKLUND TRANSFORMATION | ROGUE WAVES

INTERNAL SOLITARY WAVES | PHYSICS, MULTIDISCIPLINARY | SCHRODINGER-EQUATION | LIE SYMMETRIES | DYNAMICS | INFINITE CONSERVATION-LAWS | SYSTEMS | RATIONAL CHARACTERISTICS | BACKLUND TRANSFORMATION | ROGUE WAVES

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

NONLINEAR DYNAMICS, ISSN 0924-090X, 10/2019, Volume 98, Issue 2, pp. 1379 - 1390

In this paper, we introduce a new integrable nonlinear evolution equation in 4+1 dimensions, which is an extension of Boiti-Leon-Manna-Pempinelli equation. We...

KADOMTSEV-PETVIASHVILI | PAINLEVE ANALYSIS | TRANSFORMATION | MECHANICS | SOLITON-SOLUTIONS | (4+1)-Dimensional BLMP equation | Infinite conservation laws | Periodic soliton solution | Lump-kink solution | LUMP-KINK SOLUTIONS | Backlund transformation | ENGINEERING, MECHANICAL | Environmental law | Business schools

KADOMTSEV-PETVIASHVILI | PAINLEVE ANALYSIS | TRANSFORMATION | MECHANICS | SOLITON-SOLUTIONS | (4+1)-Dimensional BLMP equation | Infinite conservation laws | Periodic soliton solution | Lump-kink solution | LUMP-KINK SOLUTIONS | Backlund transformation | ENGINEERING, MECHANICAL | Environmental law | Business schools

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

理论物理通讯：英文版, ISSN 0253-6102, 2011, Volume 55, Issue 4, pp. 629 - 634

In this paper, an infinite sequence of conservation laws for a generalized variable-coefficient fifth-order Korteweg-de Vries equation in fluids are...

流体方程 | 解析解 | Backlund变换 | 无限序列 | 五阶KdV方程 | 德弗里斯 | 守恒定律 | 广义变系数 | infinite sequence of conservation laws | symbolic computation | wave number | variable-coefficient fifth-order Korteweg-de Vries equation in fluids | Hirota bilinear method | soliton solutions | INHOMOGENEOUS OPTICAL-FIBERS | PHYSICS, MULTIDISCIPLINARY | DEVRIES EQUATION | ION-ACOUSTIC-WAVES | SAWADA-KOTERA EQUATION | SYMBOLIC-COMPUTATION | KADOMTSEV-PETVIASHVILI EQUATION | NONLINEAR SCHRODINGER MODEL | BACKLUND TRANSFORMATION | SOLITARY WAVES | DUSTY PLASMA

流体方程 | 解析解 | Backlund变换 | 无限序列 | 五阶KdV方程 | 德弗里斯 | 守恒定律 | 广义变系数 | infinite sequence of conservation laws | symbolic computation | wave number | variable-coefficient fifth-order Korteweg-de Vries equation in fluids | Hirota bilinear method | soliton solutions | INHOMOGENEOUS OPTICAL-FIBERS | PHYSICS, MULTIDISCIPLINARY | DEVRIES EQUATION | ION-ACOUSTIC-WAVES | SAWADA-KOTERA EQUATION | SYMBOLIC-COMPUTATION | KADOMTSEV-PETVIASHVILI EQUATION | NONLINEAR SCHRODINGER MODEL | BACKLUND TRANSFORMATION | SOLITARY WAVES | DUSTY PLASMA

Journal Article