Computers and Mathematics with Applications, ISSN 0898-1221, 11/2017, Volume 74, Issue 10, pp. 2341 - 2347

Breather, lump and soliton solutions are presented via the Hirota bilinear method, to the nonlocal (2+1)-dimensional KP equation, derived from the Alice–Bob...

[formula omitted] soliton | Alice–Bob system | Nonlocal KP equation | Lump solution | X soliton | RATIONAL SOLUTIONS | WAVE | MATHEMATICS, APPLIED | SYMMETRY | HIROTA BILINEAR EQUATION | Alice-Bob system

[formula omitted] soliton | Alice–Bob system | Nonlocal KP equation | Lump solution | X soliton | RATIONAL SOLUTIONS | WAVE | MATHEMATICS, APPLIED | SYMMETRY | HIROTA BILINEAR EQUATION | Alice-Bob system

Journal Article

COMMUNICATIONS IN THEORETICAL PHYSICS, ISSN 0253-6102, 06/2019, Volume 71, Issue 6, pp. 629 - 632

An Alice-Bob Kadomtsev-Petviashivili (ABKP) equation with shifted-parity ((P) over cap (x)(s) parity with a shift for the space variable x) and delayed time...

parity and time reversal | classical prohibition | DE-VRIES EQUATION | PHYSICS, MULTIDISCIPLINARY | KP equations | nonlocal systems

parity and time reversal | classical prohibition | DE-VRIES EQUATION | PHYSICS, MULTIDISCIPLINARY | KP equations | nonlocal systems

Journal Article

Journal of Mathematical Physics, ISSN 0022-2488, 12/1997, Volume 38, Issue 12, pp. 6401 - 6427

Starting from a known Lax pair, one can get some infinitely many coupled Lax pairs, infinitely many nonlocal symmetries and infinitely many new integrable...

KORTEWEG-DEVRIES EQUATION | LINEAR EVOLUTION-EQUATIONS | DE VRIES EQUATIONS | HAMILTONIAN-SYSTEMS | K UR PHYSICS, MATHEMATICAL | KDV EQUATION | PAINLEVE PROPERTY | NONLOCAL SYMMETRIES | PHYSICS, MATHEMATICAL | KADOMTSEV-PETVIASHVILI EQUATION | BINARY DARBOUX TRANSFORMATIONS | ORDINARY DIFFERENTIAL-EQUATIONS

KORTEWEG-DEVRIES EQUATION | LINEAR EVOLUTION-EQUATIONS | DE VRIES EQUATIONS | HAMILTONIAN-SYSTEMS | K UR PHYSICS, MATHEMATICAL | KDV EQUATION | PAINLEVE PROPERTY | NONLOCAL SYMMETRIES | PHYSICS, MATHEMATICAL | KADOMTSEV-PETVIASHVILI EQUATION | BINARY DARBOUX TRANSFORMATIONS | ORDINARY DIFFERENTIAL-EQUATIONS

Journal Article

Abstract and Applied Analysis, ISSN 1085-3375, 2013, Volume 2013, pp. 1 - 11

We study here the Lie symmetries, conservation laws, reductions, and new exact solutions of (2 + 1) dimensional Zakharov-Kuznetsov (ZK), Gardner...

MATHEMATICS | MATHEMATICS, APPLIED | WAVE EQUATIONS | SINE-COSINE METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | CONSERVATION-LAWS | NONLOCAL SYMMETRIES | ASSOCIATION | Trigonometrical functions | Vector spaces | Research | Mathematical research | Differential equations | Conservation laws | Reduction | Theorems | Mathematical analysis | Exact solutions | Mathematical models | Symmetry

MATHEMATICS | MATHEMATICS, APPLIED | WAVE EQUATIONS | SINE-COSINE METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | CONSERVATION-LAWS | NONLOCAL SYMMETRIES | ASSOCIATION | Trigonometrical functions | Vector spaces | Research | Mathematical research | Differential equations | Conservation laws | Reduction | Theorems | Mathematical analysis | Exact solutions | Mathematical models | Symmetry

Journal Article

Wave Motion, ISSN 0165-2125, 12/2014, Volume 51, Issue 8, pp. 1298 - 1308

In nonlinear science, the interactions among solitons are well studied because the multiple soliton solutions can be obtained by various effective methods....

Soliton–Boussinesq wave | Symmetry reductions | Nonlocal symmetries | Soliton–periodic wave | KP equation | Soliton–KdV wave | Soliton-KdV wave | Soliton-periodic wave | Soliton-Boussinesq wave | DARBOUX TRANSFORMATION | PHYSICS, MULTIDISCIPLINARY | SEARCH | 3-SOLITON CONDITION | ACOUSTICS | MECHANICS | SOLITONS | CONSTRUCTION | BILINEAR EQUATIONS | PAINLEVE PROPERTY | KDV | Wave motion | Mathematical analysis | Solitons | Nonlinearity | Mathematical models | Transformations | Solitary waves | Invariants

Soliton–Boussinesq wave | Symmetry reductions | Nonlocal symmetries | Soliton–periodic wave | KP equation | Soliton–KdV wave | Soliton-KdV wave | Soliton-periodic wave | Soliton-Boussinesq wave | DARBOUX TRANSFORMATION | PHYSICS, MULTIDISCIPLINARY | SEARCH | 3-SOLITON CONDITION | ACOUSTICS | MECHANICS | SOLITONS | CONSTRUCTION | BILINEAR EQUATIONS | PAINLEVE PROPERTY | KDV | Wave motion | Mathematical analysis | Solitons | Nonlinearity | Mathematical models | Transformations | Solitary waves | Invariants

Journal Article

Kinetic and Related Models, ISSN 1937-5093, 12/2013, Volume 6, Issue 4, pp. 989 - 1009

We consider in this paper the Full Dispersion Kadomtsev-Petviashvili Equation (FDKP) introduced in [19] in order to overcome some shortcomings of the classical...

Water waves | Whitham equation | KP equation | Weakly transverse waves | Full dispersion | Nonlocal dispersion | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | full dispersion | STABILITY | SOLITARY-WAVE SOLUTIONS | water waves | nonlocal dispersion | weakly transverse waves

Water waves | Whitham equation | KP equation | Weakly transverse waves | Full dispersion | Nonlocal dispersion | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | full dispersion | STABILITY | SOLITARY-WAVE SOLUTIONS | water waves | nonlocal dispersion | weakly transverse waves

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 2000, Volume 5, Issue 1, pp. 31 - 35

With the aid of MATHEMATICA, the idea of improved homogeneous balance method is extended to (2+1)-dimensional variable coefficients KP equation. As a result,...

variable coefficient generalized KP equation | soliton | exact solution | nonlocal symmetry | Bäcklund transformation | Soliton | Variable coefficient generalized KP equation | Non-local symmetry | Exact solution

variable coefficient generalized KP equation | soliton | exact solution | nonlocal symmetry | Bäcklund transformation | Soliton | Variable coefficient generalized KP equation | Non-local symmetry | Exact solution

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 6/2007, Volume 272, Issue 2, pp. 469 - 505

The algebro-geometric approach for integrability of semi-Hamiltonian hydrodynamic type systems is presented. The class of symmetric hydrodynamic type systems...

Quantum Computing, Information and Physics | Relativity and Cosmology | Mathematical and Computational Physics | Quantum Physics | Physics | Statistical Physics | Complexity | REDUCTIONS | BENNEY EQUATIONS | MODELS | KP EQUATION | HIERARCHIES | CHAINS | NONLOCAL POISSON BRACKETS | PHYSICS, MATHEMATICAL | Physics - Exactly Solvable and Integrable Systems

Quantum Computing, Information and Physics | Relativity and Cosmology | Mathematical and Computational Physics | Quantum Physics | Physics | Statistical Physics | Complexity | REDUCTIONS | BENNEY EQUATIONS | MODELS | KP EQUATION | HIERARCHIES | CHAINS | NONLOCAL POISSON BRACKETS | PHYSICS, MATHEMATICAL | Physics - Exactly Solvable and Integrable Systems

Journal Article

中国物理B：英文版, ISSN 1674-1056, 2014, Volume 23, Issue 10, pp. 1 - 6

The residual symmetry relating to the truncated Painlev6 expansion of the Kadomtsev-Petviashvili （KP） equation is nonlocal, which is localized in this paper by...

一般形式 | 李群方法 | 相互作用 | KP方程 | 交互 | 对称性 | 时间系统 | 使用标准 | SOLITON HIERARCHY | localization procedure | residual symmetry | PHYSICS, MULTIDISCIPLINARY | Kadomtsev-Petviashvili equation | symmetry reduction solution | Backlund transformation | NONLOCAL SYMMETRIES | Reduction | Dependent variables | Mathematical analysis | Lie groups | Solitons | Standards | Symmetry | Physics - Exactly Solvable and Integrable Systems

一般形式 | 李群方法 | 相互作用 | KP方程 | 交互 | 对称性 | 时间系统 | 使用标准 | SOLITON HIERARCHY | localization procedure | residual symmetry | PHYSICS, MULTIDISCIPLINARY | Kadomtsev-Petviashvili equation | symmetry reduction solution | Backlund transformation | NONLOCAL SYMMETRIES | Reduction | Dependent variables | Mathematical analysis | Lie groups | Solitons | Standards | Symmetry | Physics - Exactly Solvable and Integrable Systems

Journal Article

International Journal of Non-Linear Mechanics, ISSN 0020-7462, 03/2016, Volume 79, pp. 1 - 9

A geometrically nonlinear large deformation analysis of SLGSs is presented using the element-free kp-Ritz method. Classical plate theory (CLP) is applied to...

Nonlinear large deformation | SLGSs | Element-free kp-Ritz method | Nonlocal elasticity theory | GRAPHENE SHEETS | ELASTICITY | MECHANICS | NONLINEAR-ANALYSIS | VIBRATION | Plate theory | Nonlinear equations | Deformation | Mathematical analysis | Small scale | Nonlinearity | Mathematical models | Computational efficiency

Nonlinear large deformation | SLGSs | Element-free kp-Ritz method | Nonlocal elasticity theory | GRAPHENE SHEETS | ELASTICITY | MECHANICS | NONLINEAR-ANALYSIS | VIBRATION | Plate theory | Nonlinear equations | Deformation | Mathematical analysis | Small scale | Nonlinearity | Mathematical models | Computational efficiency

Journal Article

Nonlinearity, ISSN 0951-7715, 10/2018, Volume 31, Issue 12, pp. 5385 - 5409

General soliton solutions to a nonlocal nonlinear Schrodinger (NLS) equation with PT-symmetry for both zero and nonzero boundary conditions are considered via...

the KP hierarchy reduction method | nonlocal nonlinear Schrodiinger equation | soliton solutions with zero and nonzero boundary conditions | Hirota's bilinear method | MATHEMATICS, APPLIED | INVERSE SCATTERING TRANSFORM | KP HIERARCHY | DE-VRIES EQUATION | PHYSICS, MATHEMATICAL | MANAKOV SYSTEM | OPTICAL PULSES | TRANSMISSION | WAVES | DYNAMICS | DISPERSIVE DIELECTRIC FIBERS

the KP hierarchy reduction method | nonlocal nonlinear Schrodiinger equation | soliton solutions with zero and nonzero boundary conditions | Hirota's bilinear method | MATHEMATICS, APPLIED | INVERSE SCATTERING TRANSFORM | KP HIERARCHY | DE-VRIES EQUATION | PHYSICS, MATHEMATICAL | MANAKOV SYSTEM | OPTICAL PULSES | TRANSMISSION | WAVES | DYNAMICS | DISPERSIVE DIELECTRIC FIBERS

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 07/2018, Volume 93, Issue 2, pp. 721 - 731

We investigate a -dimensional nonlocal nonlinear Schrodinger equation with the self-induced parity-time symmetric potential. By employing the Hirota's bilinear...

Hirota’s bilinear method | Soliton solution | KP hierarchy reduction method | (2 + 1) -Dimensional nonlocal nonlinear Schrödinger | TRANSFORMATION | MECHANICS | (2+1)-Dimensional nonlocal nonlinear Schrodinger equation | Hirota's bilinear method | DIFFERENTIAL-EQUATION | DYNAMICS | MEDIA | MODULATION | ENGINEERING, MECHANICAL | ROGUE WAVES | Information science | Boundary conditions | Solitary waves | Schroedinger equation

Hirota’s bilinear method | Soliton solution | KP hierarchy reduction method | (2 + 1) -Dimensional nonlocal nonlinear Schrödinger | TRANSFORMATION | MECHANICS | (2+1)-Dimensional nonlocal nonlinear Schrodinger equation | Hirota's bilinear method | DIFFERENTIAL-EQUATION | DYNAMICS | MEDIA | MODULATION | ENGINEERING, MECHANICAL | ROGUE WAVES | Information science | Boundary conditions | Solitary waves | Schroedinger equation

Journal Article

NONLINEAR DYNAMICS, ISSN 0924-090X, 11/2018, Volume 94, Issue 3, pp. 2177 - 2189

General bright and dark soliton solutions to the partial reverse space-time nonlocal Mel'nikov equation with parity-time symmetry are constructed by the Hirota...

Soliton solution | RATIONAL SOLUTIONS | WAVES | MECHANICS | Hirota's bilinear method | KP hierarchy reduction method | Partial reverse space-time nonlocal Mel'nikov equation | ORBITAL STABILITY | ENGINEERING, MECHANICAL | Information science

Soliton solution | RATIONAL SOLUTIONS | WAVES | MECHANICS | Hirota's bilinear method | KP hierarchy reduction method | Partial reverse space-time nonlocal Mel'nikov equation | ORBITAL STABILITY | ENGINEERING, MECHANICAL | Information science

Journal Article

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 05/2012, Volume 85, Issue 5, p. 056607

In nonlinear science, it is very difficult to find exact interaction solutions among solitons and other kinds of complicated waves such as cnoidal waves and...

INTEGRABLE MODELS | SOLITONS | GORDON EQUATION | PHYSICS, FLUIDS & PLASMAS | KDV EQUATION | EXTENSION | CONSERVATION-LAWS | NONLOCAL SYMMETRIES | PHYSICS, MATHEMATICAL | TRANSFORMATIONS | HIERARCHY

INTEGRABLE MODELS | SOLITONS | GORDON EQUATION | PHYSICS, FLUIDS & PLASMAS | KDV EQUATION | EXTENSION | CONSERVATION-LAWS | NONLOCAL SYMMETRIES | PHYSICS, MATHEMATICAL | TRANSFORMATIONS | HIERARCHY

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 7/2018, Volume 93, Issue 2, pp. 721 - 731

We investigate a $$(2+1)$$ (2+1) -dimensional nonlocal nonlinear Schrödinger equation with the self-induced parity-time symmetric potential. By employing the...

(2+1)$$ ( 2 + 1 ) -Dimensional nonlocal nonlinear Schrödinger | Engineering | Vibration, Dynamical Systems, Control | Soliton solution | Classical Mechanics | Hirota’s bilinear method | Automotive Engineering | Mechanical Engineering | KP hierarchy reduction method

(2+1)$$ ( 2 + 1 ) -Dimensional nonlocal nonlinear Schrödinger | Engineering | Vibration, Dynamical Systems, Control | Soliton solution | Classical Mechanics | Hirota’s bilinear method | Automotive Engineering | Mechanical Engineering | KP hierarchy reduction method

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 04/2016, Volume 49, Issue 20, p. 205202

Asymptotic reductions of a defocusing nonlocal nonlinear Schrdinger model in (3 + 1)-dimensions, in both Cartesian and cylindrical geometry, are presented....

asymptotic analysis | nonlocal NLS | solitons | SOLITARY WAVES | PHYSICS, MULTIDISCIPLINARY | RING DARK SOLITONS | MULTISCALE EXPANSIONS | MULTIDIMENSIONAL SOLITONS | OPTICAL MEDIA | NEMATICONS | PHYSICS, MATHEMATICAL | PROPAGATION

asymptotic analysis | nonlocal NLS | solitons | SOLITARY WAVES | PHYSICS, MULTIDISCIPLINARY | RING DARK SOLITONS | MULTISCALE EXPANSIONS | MULTIDIMENSIONAL SOLITONS | OPTICAL MEDIA | NEMATICONS | PHYSICS, MATHEMATICAL | PROPAGATION

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 11/2018, Volume 94, Issue 3, pp. 2177 - 2189

General bright and dark soliton solutions to the partial reverse space–time nonlocal Mel’nikov equation with parity–time symmetry are constructed by the Hirota...

Engineering | Vibration, Dynamical Systems, Control | Soliton solution | Partial reverse space–time nonlocal Mel’nikov equation | Classical Mechanics | Hirota’s bilinear method | Automotive Engineering | Mechanical Engineering | KP hierarchy reduction method | Mathematical analysis | Solitary waves | Exact solutions

Engineering | Vibration, Dynamical Systems, Control | Soliton solution | Partial reverse space–time nonlocal Mel’nikov equation | Classical Mechanics | Hirota’s bilinear method | Automotive Engineering | Mechanical Engineering | KP hierarchy reduction method | Mathematical analysis | Solitary waves | Exact solutions

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 04/2019, Volume 69, pp. 45 - 57

The present article is devoted to obtain some invariant solutions of (2+1)–dimensional Gardner equation by using similarity transformation method. The equation...

Numerical simulation | Gardner equation | Lie group theory | Invariant solutions | SYSTEM | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | MODEL | PHYSICS, MATHEMATICAL | KINK SOLUTIONS | PAINLEVE ANALYSIS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SOLITONS | REDUCTION | GROUP CLASSIFICATION | COEFFICIENTS | KDV | NONLOCAL SYMMETRY | Numerical analysis | Differential equations

Numerical simulation | Gardner equation | Lie group theory | Invariant solutions | SYSTEM | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | MODEL | PHYSICS, MATHEMATICAL | KINK SOLUTIONS | PAINLEVE ANALYSIS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | SOLITONS | REDUCTION | GROUP CLASSIFICATION | COEFFICIENTS | KDV | NONLOCAL SYMMETRY | Numerical analysis | Differential equations

Journal Article

19.
Full Text
Free vibration analysis of bilayer graphene sheets subjected to in-plane magnetic fields

Composite Structures, ISSN 0263-8223, 06/2016, Volume 144, pp. 86 - 95

Bilayer graphene sheets (BLGSs) have attracted increasing attention due to their unique and highly valuable properties. The present study investigates the...

Bilayer graphene sheets | Ritz method | Nonlocal theory | Free vibration | Magnetic field | RESONATORS | SKEW PLATES | EQUATIONS | MATERIALS SCIENCE, COMPOSITES | KP-RITZ METHOD | NONLOCAL ELASTICITY THEORY | MODEL | WALLED CARBON NANOTUBES | KERNEL PARTICLE METHODS | NANORIBBONS | SEPARATION | Vibration | Magnetic fields | Graphene | Analysis | Graphite | Information science | Interlayers | Asymptotic properties | Vibration mode | Boundary conditions | Aspect ratio

Bilayer graphene sheets | Ritz method | Nonlocal theory | Free vibration | Magnetic field | RESONATORS | SKEW PLATES | EQUATIONS | MATERIALS SCIENCE, COMPOSITES | KP-RITZ METHOD | NONLOCAL ELASTICITY THEORY | MODEL | WALLED CARBON NANOTUBES | KERNEL PARTICLE METHODS | NANORIBBONS | SEPARATION | Vibration | Magnetic fields | Graphene | Analysis | Graphite | Information science | Interlayers | Asymptotic properties | Vibration mode | Boundary conditions | Aspect ratio

Journal Article

Engineering Analysis with Boundary Elements, ISSN 0955-7997, 07/2015, Volume 56, pp. 90 - 97

In this paper, an implementation of the kp-Ritz method with the nonlocal continuum model as an element-free computational framework has been performed to...

Single-layered graphene sheet | Free vibration analysis | Element-free kp-Ritz method | Nonlocal elasticity theory | GRADED CYLINDRICAL PANELS | EQUATIONS | PLATES | NANOCONES | WALLED CARBON NANOTUBES | KERNEL PARTICLE METHODS | ELASTICITY | ORDER GRADIENT THEORY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | MOVING KRIGING INTERPOLATION | FREE GALERKIN METHOD | Models | Vibration | Graphene | Analysis | Methods | Graphite | Plate theory | Free vibration | Computation | Continuums | Boundary conditions | Mathematical models

Single-layered graphene sheet | Free vibration analysis | Element-free kp-Ritz method | Nonlocal elasticity theory | GRADED CYLINDRICAL PANELS | EQUATIONS | PLATES | NANOCONES | WALLED CARBON NANOTUBES | KERNEL PARTICLE METHODS | ELASTICITY | ORDER GRADIENT THEORY | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | ENGINEERING, MULTIDISCIPLINARY | MOVING KRIGING INTERPOLATION | FREE GALERKIN METHOD | Models | Vibration | Graphene | Analysis | Methods | Graphite | Plate theory | Free vibration | Computation | Continuums | Boundary conditions | Mathematical models

Journal Article

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