2012, Mathematical surveys and monographs, ISBN 9780821889817, Volume 183, vii, 317

Book

SpringerPlus, ISSN 2193-1801, 12/2014, Volume 3, Issue 1, pp. 1 - 6

In this article, a new extended (G′/G) -expansion method has been proposed for constructing more general exact traveling wave solutions of nonlinear evolution...

Homogeneous balance | (G’/G) -expansion method | Traveling wave solutions | (3 + 1)-dimensional potential-YTSF equation | Science, general | (G'/G)-expansion method | (G '/G)-expansion method | (3+1)-dimensional potential-YTSF equation | TRAVELING-WAVE SOLUTIONS | MULTIDISCIPLINARY SCIENCES | EXPLICIT

Homogeneous balance | (G’/G) -expansion method | Traveling wave solutions | (3 + 1)-dimensional potential-YTSF equation | Science, general | (G'/G)-expansion method | (G '/G)-expansion method | (3+1)-dimensional potential-YTSF equation | TRAVELING-WAVE SOLUTIONS | MULTIDISCIPLINARY SCIENCES | EXPLICIT

Journal Article

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, ISSN 1364-503X, 04/2013, Volume 371, Issue 1989, p. 20120059

The complex PT-symmetric nonlinear wave models have drawn much attention in recent years since the complex PT-symmetric extensions of the Korteweg-de Vries...

CLASSICAL TRAJECTORIES | exact solutions | MULTIDISCIPLINARY SCIENCES | complex PT-symmetric Burgers equation | REAL | complex PT symmetry | WEAK PSEUDO-HERMITICITY | HAMILTONIANS | SPECTRUM | OPERATORS | nonlinear Schrodinger equation with complex PT-symmetric potentials

CLASSICAL TRAJECTORIES | exact solutions | MULTIDISCIPLINARY SCIENCES | complex PT-symmetric Burgers equation | REAL | complex PT symmetry | WEAK PSEUDO-HERMITICITY | HAMILTONIANS | SPECTRUM | OPERATORS | nonlinear Schrodinger equation with complex PT-symmetric potentials

Journal Article

Annals of Physics, ISSN 0003-4916, 02/2014, Volume 341, pp. 142 - 152

The one-to-one correspondence between a (3+1)-dimensional variable-coefficient nonlinear Schrödinger equation with linear and parabolic potentials and a...

Superposed Akhmediev breather | Controllable dynamical behaviors | Nonlinear Schrödinger equation | PHYSICS, MULTIDISCIPLINARY | Nonlinear Schrodinger equation | ROGUE WAVES | FIBER | SOLITONS | PLASMA | MODULATION INSTABILITY | SOLITARY WAVES | DYNAMICS | LATTICES | SCATTERING | Chirp | Diffraction | Nonlinearity | Controllability | Evolution | Schroedinger equation | Terminals | Gain | MATHEMATICAL SOLUTIONS | EXCITATION | PEAKS | NONLINEAR PROBLEMS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | EQUATIONS | DIFFRACTION | AMPLITUDES | POTENTIALS | GAIN

Superposed Akhmediev breather | Controllable dynamical behaviors | Nonlinear Schrödinger equation | PHYSICS, MULTIDISCIPLINARY | Nonlinear Schrodinger equation | ROGUE WAVES | FIBER | SOLITONS | PLASMA | MODULATION INSTABILITY | SOLITARY WAVES | DYNAMICS | LATTICES | SCATTERING | Chirp | Diffraction | Nonlinearity | Controllability | Evolution | Schroedinger equation | Terminals | Gain | MATHEMATICAL SOLUTIONS | EXCITATION | PEAKS | NONLINEAR PROBLEMS | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | EQUATIONS | DIFFRACTION | AMPLITUDES | POTENTIALS | GAIN

Journal Article

2008, Proceedings of symposia in pure mathematics, ISBN 0821844245, Volume 79., xvii, 423

Book

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2008, Volume 222, Issue 2, pp. 333 - 350

In this paper, we elaborated a spectral collocation method based on differentiated Chebyshev polynomials to obtain numerical solutions for some different kinds...

2D Burgers’ equation | Chebyshev spectral collocation method | 1D Burgers’ equation | Numerical solutions | Coupled Burgers’ equations | System of 2D Burgers’ equations | KdV–Burgers’ equation | KdV-Burgers' equation | 1D Burgers' equation | 2D Burgers' equation | System of 2D Burgers' equations | Coupled Burgers' equations | KdV-Burger' equation | INVARIANT SOLUTIONS | MATHEMATICS, APPLIED | PSEUDO-SPHERICAL SURFACES | SIMILARITY SOLUTIONS | DIFFUSION EQUATION | 1D Bugers' equation | System of 2D Burgers' equation | TRAVELING-WAVE SOLUTIONS | POTENTIAL SYMMETRIES | BACKLUND-TRANSFORMATIONS | NUMERICAL-SOLUTIONS | ADOMIAN DECOMPOSITION METHOD | NONLINEAR EVOLUTION-EQUATIONS

2D Burgers’ equation | Chebyshev spectral collocation method | 1D Burgers’ equation | Numerical solutions | Coupled Burgers’ equations | System of 2D Burgers’ equations | KdV–Burgers’ equation | KdV-Burgers' equation | 1D Burgers' equation | 2D Burgers' equation | System of 2D Burgers' equations | Coupled Burgers' equations | KdV-Burger' equation | INVARIANT SOLUTIONS | MATHEMATICS, APPLIED | PSEUDO-SPHERICAL SURFACES | SIMILARITY SOLUTIONS | DIFFUSION EQUATION | 1D Bugers' equation | System of 2D Burgers' equation | TRAVELING-WAVE SOLUTIONS | POTENTIAL SYMMETRIES | BACKLUND-TRANSFORMATIONS | NUMERICAL-SOLUTIONS | ADOMIAN DECOMPOSITION METHOD | NONLINEAR EVOLUTION-EQUATIONS

Journal Article

2011, ISBN 9789814360739, xiv, 283

Book

Engineering with Computers, ISSN 0177-0667, 1/2018, Volume 34, Issue 1, pp. 203 - 213

In this paper, the local boundary integral equation (LBIE) method based on generalized moving least squares (GMLS) is proposed for solving extended...

Direct local boundary integral equation method (DLBIE) | LBIE-radial point interpolation (LBIE-RPI) method | Systems Theory, Control | Classical Mechanics | Extended Fisher–Kolmogorov (EFK) equation | LBIE-moving Kriging (LBIE-MK) method | Calculus of Variations and Optimal Control; Optimization | Computer-Aided Engineering (CAD, CAE) and Design | Computer Science | Mathematical and Computational Engineering | LBIE-moving least squares (LBIE-MLS) method | 65M99 | 65N99 | Math. Applications in Chemistry | DIFFUSION EQUATIONS | 2-DIMENSIONAL SCHRODINGER-EQUATION | ELASTODYNAMIC ANALYSIS | POINT INTERPOLATION | Extended Fisher-Kolmogorov (EFK) equation | VELOCITY SELECTION | POTENTIAL PROBLEMS | ENGINEERING, MECHANICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SIVASHINSKY EQUATION | MARGINAL STABILITY | PETROV-GALERKIN METHOD | AMERICAN OPTIONS | Methods | Differential equations | Nonlinear equations | Partial differential equations | Nonlinear differential equations | Numerical methods | Kriging | Finite element method | Mathematical analysis | Integral equations | Efficiency | Meshless methods | Least squares | Mathematical models | Computational efficiency | Computing time | Boundary element method | Shape functions

Direct local boundary integral equation method (DLBIE) | LBIE-radial point interpolation (LBIE-RPI) method | Systems Theory, Control | Classical Mechanics | Extended Fisher–Kolmogorov (EFK) equation | LBIE-moving Kriging (LBIE-MK) method | Calculus of Variations and Optimal Control; Optimization | Computer-Aided Engineering (CAD, CAE) and Design | Computer Science | Mathematical and Computational Engineering | LBIE-moving least squares (LBIE-MLS) method | 65M99 | 65N99 | Math. Applications in Chemistry | DIFFUSION EQUATIONS | 2-DIMENSIONAL SCHRODINGER-EQUATION | ELASTODYNAMIC ANALYSIS | POINT INTERPOLATION | Extended Fisher-Kolmogorov (EFK) equation | VELOCITY SELECTION | POTENTIAL PROBLEMS | ENGINEERING, MECHANICAL | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | SIVASHINSKY EQUATION | MARGINAL STABILITY | PETROV-GALERKIN METHOD | AMERICAN OPTIONS | Methods | Differential equations | Nonlinear equations | Partial differential equations | Nonlinear differential equations | Numerical methods | Kriging | Finite element method | Mathematical analysis | Integral equations | Efficiency | Meshless methods | Least squares | Mathematical models | Computational efficiency | Computing time | Boundary element method | Shape functions

Journal Article

Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 08/2016, Volume 455, pp. 44 - 51

The nonlinear three-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov (mKdV–ZK) equation governs the behavior of weakly nonlinear ion-acoustic waves...

Magnetized electron–positron plasma | Modified Korteweg–de Vries–Zakharov–Kuznetsov equation | Ion-acoustic waves | Fractional extended direct algebraic method | Magnetized electron-positron plasma | Modified Korteweg-de Vries-Zakharov-Kuznetsov equation | PHYSICS, MULTIDISCIPLINARY | ACOUSTIC SOLITARY WAVES | BURGERS EQUATION | DOUBLE-LAYERS | INSTABILITIES | Electric fields | Electric potential | Perturbation methods | Mathematical analysis | Traveling waves | Nonlinearity | Electrostatic fields | Electron-positron plasmas | Three dimensional

Magnetized electron–positron plasma | Modified Korteweg–de Vries–Zakharov–Kuznetsov equation | Ion-acoustic waves | Fractional extended direct algebraic method | Magnetized electron-positron plasma | Modified Korteweg-de Vries-Zakharov-Kuznetsov equation | PHYSICS, MULTIDISCIPLINARY | ACOUSTIC SOLITARY WAVES | BURGERS EQUATION | DOUBLE-LAYERS | INSTABILITIES | Electric fields | Electric potential | Perturbation methods | Mathematical analysis | Traveling waves | Nonlinearity | Electrostatic fields | Electron-positron plasmas | Three dimensional

Journal Article

Electronic Journal of Differential Equations, ISSN 1072-6691, 02/2018, Volume 2018, Issue 55, pp. 1 - 52

This article studies the existence and nonexistence of global solutions to the initial boundary value problems for semilinear wave and heat equation, and for...

Global solution | Semilinear parabolic equation | Nonlinear Schrodinger equation | Potential well | Semilinear hyperbolic equation | EXISTENCE | MATHEMATICS, APPLIED | INSTABILITY | nonlinear Schrodinger equation | semilinear parabolic equation | CAUCHY-PROBLEM | potential well | MATHEMATICS | NONLINEAR SCHRODINGER | WAVE-EQUATIONS | global solution | TIME BLOW-UP | KLEIN-GORDON EQUATIONS

Global solution | Semilinear parabolic equation | Nonlinear Schrodinger equation | Potential well | Semilinear hyperbolic equation | EXISTENCE | MATHEMATICS, APPLIED | INSTABILITY | nonlinear Schrodinger equation | semilinear parabolic equation | CAUCHY-PROBLEM | potential well | MATHEMATICS | NONLINEAR SCHRODINGER | WAVE-EQUATIONS | global solution | TIME BLOW-UP | KLEIN-GORDON EQUATIONS

Journal Article

2016, Association for Women in Mathematics Series, ISBN 9783319309590, Volume 4, 369

Covering a range of subjects from operator theory and classical harmonic analysis to Banach space theory, this book contains survey and expository articles by...

Abstract Harmonic Analysis | Operator Theory | Mathematics | Mathematical Physics | Harmonic analysis

Abstract Harmonic Analysis | Operator Theory | Mathematics | Mathematical Physics | Harmonic analysis

eBook

12.
Full Text
Boundary regularized integral equation formulation of the Helmholtz equation in acoustics

Royal Society Open Science, ISSN 2054-5703, 01/2015, Volume 2, Issue 1, p. 140520

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals...

Wave equation | Helmholtz equation | Singularity removal | Boundary integral equation | POTENTIAL-THEORY | boundary integral equation | MULTIDISCIPLINARY SCIENCES | singularity removal | wave equation

Wave equation | Helmholtz equation | Singularity removal | Boundary integral equation | POTENTIAL-THEORY | boundary integral equation | MULTIDISCIPLINARY SCIENCES | singularity removal | wave equation

Journal Article

13.
Full Text
2+1 flavors QCD equation of state at zero temperature within Dyson–Schwinger equations

International Journal of Modern Physics A, ISSN 0217-751X, 12/2015, Volume 30, Issue 36, p. 1550217

Within the framework of Dyson–Schwinger equations (DSEs), we discuss the equation of state (EOS) and quark number densities of 2+1 flavors, that is to say, u ,...

quark number density | Equation of state | Dyson-Schwinger equations | TRANSITION | DENSITY | WIGNER SOLUTION | PHYSICS, NUCLEAR | MODEL | QUARK MATTER | SYMMETRY-BREAKING | PHYSICS, PARTICLES & FIELDS | Quarks | Physics - High Energy Physics - Phenomenology

quark number density | Equation of state | Dyson-Schwinger equations | TRANSITION | DENSITY | WIGNER SOLUTION | PHYSICS, NUCLEAR | MODEL | QUARK MATTER | SYMMETRY-BREAKING | PHYSICS, PARTICLES & FIELDS | Quarks | Physics - High Energy Physics - Phenomenology

Journal Article

14.
Full Text
The Laplace Equation

: Boundary Value Problems on Bounded and Unbounded Lipschitz Domains

2018, 1st ed. 2018, ISBN 9783319743066, 669

This book is devoted to boundary value problems of the Laplace equation on bounded and unbounded Lipschitz domains. It studies the Dirichlet problem, the...

Potential Theory | Mathematics | Partial Differential Equations | Neumann problem | Dirichlet problem | Poisson equation | Transmission problem | Derivative oblique problem | Robin problem

Potential Theory | Mathematics | Partial Differential Equations | Neumann problem | Dirichlet problem | Poisson equation | Transmission problem | Derivative oblique problem | Robin problem

eBook

Physics Letters A, ISSN 0375-9601, 07/2017, Volume 381, Issue 25-26, pp. 2050 - 2054

New exact analytical bound-state solutions of the radial Dirac equation in 3+1 dimensions for two sets of couplings and radial potential functions are obtained...

Dirac equation | Morse potential | STEP-DOWN OPERATORS | LAPLACE TRANSFORM | STATES | PHYSICS, MULTIDISCIPLINARY | SINGULAR HARMONIC-OSCILLATOR | LADDER OPERATORS | PLUS

Dirac equation | Morse potential | STEP-DOWN OPERATORS | LAPLACE TRANSFORM | STATES | PHYSICS, MULTIDISCIPLINARY | SINGULAR HARMONIC-OSCILLATOR | LADDER OPERATORS | PLUS

Journal Article

1976, ISBN 9780121604509, xi, 320

Book

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2008, Volume 345, Issue 1, pp. 90 - 108

In this paper we study the nonlinear Schrödinger–Maxwell equations { − Δ u + V ( x ) u + ϕ u = | u | p − 1 u in R 3 , − Δ ϕ = u 2 in R 3 . If V is a positive...

Nonlinear Schrödinger–Maxwell equations | Ground state solutions | Nonlinear Schrödinger-Maxwell equations | SYSTEM | EXISTENCE | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | SCALAR FIELD-EQUATIONS | NONEXISTENCE | nonlinear schrodinger-maxwell equations | COMPETING POTENTIAL FUNCTIONS | POSITIVE SOLUTIONS | CALCULUS | ground state solutions | CONCENTRATION-COMPACTNESS PRINCIPLE | MATHEMATICS | MULTIPLE SOLITARY WAVES

Nonlinear Schrödinger–Maxwell equations | Ground state solutions | Nonlinear Schrödinger-Maxwell equations | SYSTEM | EXISTENCE | MATHEMATICS, APPLIED | KLEIN-GORDON-MAXWELL | SCALAR FIELD-EQUATIONS | NONEXISTENCE | nonlinear schrodinger-maxwell equations | COMPETING POTENTIAL FUNCTIONS | POSITIVE SOLUTIONS | CALCULUS | ground state solutions | CONCENTRATION-COMPACTNESS PRINCIPLE | MATHEMATICS | MULTIPLE SOLITARY WAVES

Journal Article

The Journal of Chemical Physics, ISSN 0021-9606, 12/2018, Volume 149, Issue 24, p. 244116

The free-complement (FC) theory for solving the Schrödinger equation (SE) was applied to calculate the potential energy curves of the ground and excited states...

Potential energy | Negative ions | Mathematical analysis | Hydrogen | Angular momentum | Atomic states | Schroedinger equation

Potential energy | Negative ions | Mathematical analysis | Hydrogen | Angular momentum | Atomic states | Schroedinger equation

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 01/2017, Volume 73, Issue 2, pp. 253 - 260

In this paper, the Lie symmetry analysis method has been proposed for finding similarity reduction and exact solutions of nonlinear evolution equation. Here...

Lie symmetries analysis method | (3[formula omitted]1) dimensional Yu–Toda–Sasa–Fukuyama (YTFS) equation | Infinitesimal generator | Tanh method | (3+1) dimensional Yu–Toda–Sasa–Fukuyama (YTFS) equation | MATHEMATICS, APPLIED | SOLITON-SOLUTIONS | BOGOYAVLENSKII-SCHIFF | EXP-FUNCTION METHOD | POTENTIAL-YTSF EQUATION | (3+1) dimensional Yu Toda Sasa Fukuyama (YTFS) equation | WAVE SOLUTIONS | NONLINEAR EVOLUTION-EQUATIONS | Algebra | Differential equations

Lie symmetries analysis method | (3[formula omitted]1) dimensional Yu–Toda–Sasa–Fukuyama (YTFS) equation | Infinitesimal generator | Tanh method | (3+1) dimensional Yu–Toda–Sasa–Fukuyama (YTFS) equation | MATHEMATICS, APPLIED | SOLITON-SOLUTIONS | BOGOYAVLENSKII-SCHIFF | EXP-FUNCTION METHOD | POTENTIAL-YTSF EQUATION | (3+1) dimensional Yu Toda Sasa Fukuyama (YTFS) equation | WAVE SOLUTIONS | NONLINEAR EVOLUTION-EQUATIONS | Algebra | Differential equations

Journal Article

2007, Birkhäuser advanced texts, ISBN 3764384417, xi, 584

Book