2015, ISBN 9781470417086, xxi, 253 p., 16 unnumbered p.s of plates

Lax, Peter D | Partial differential equations -- Hyperbolic equations and systems -- First-order hyperbolic systems | History and biography -- History of mathematics and mathematicians -- Biographies, obituaries, personalia, bibliographies | Partial differential equations -- Representations of solutions -- Soliton solutions | Partial differential equations -- General topics -- Propagation of singularities | Numerical analysis -- Partial differential equations, initial value and time-dependent initial-boundary value problems -- Finite difference methods | Partial differential equations -- Equations of mathematical physics and other areas of application -- KdV-like equations (Korteweg-de Vries) | History and biography -- History of mathematics and mathematicians -- Schools of mathematics | Partial differential equations -- Hyperbolic equations and systems -- Wave equation | Fluid mechanics -- Shock waves and blast waves -- Shock waves and blast waves | Mathematicians

Book

Computers and Mathematics with Applications, ISSN 0898-1221, 07/2015, Volume 70, Issue 2, pp. 158 - 166

In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics, namely the time fractional...

Improved fractional sub-equation method | Modified Riemann–Liouville derivative | space–time fractional modified KdV–Zakharov–Kuznetsov (mKdV–ZK) equation | Time fractional KdV–Zakharov–Kuznetsov (KdV–ZK) equation | Mittag-Leffler function | space-time fractional modified KdV-Zakharov-Kuznetsov (mKdV-ZK) equation | Time fractional KdV-Zakharov-Kuznetsov (KdV-ZK) equation | Modified Riemann-Liouville derivative | MATHEMATICS, APPLIED | DIFFERENTIAL-DIFFERENCE EQUATION | Nonlinear evolution equations | Construction | Mathematical models | Derivatives | Mathematical analysis | Exact solutions

Improved fractional sub-equation method | Modified Riemann–Liouville derivative | space–time fractional modified KdV–Zakharov–Kuznetsov (mKdV–ZK) equation | Time fractional KdV–Zakharov–Kuznetsov (KdV–ZK) equation | Mittag-Leffler function | space-time fractional modified KdV-Zakharov-Kuznetsov (mKdV-ZK) equation | Time fractional KdV-Zakharov-Kuznetsov (KdV-ZK) equation | Modified Riemann-Liouville derivative | MATHEMATICS, APPLIED | DIFFERENTIAL-DIFFERENCE EQUATION | Nonlinear evolution equations | Construction | Mathematical models | Derivatives | Mathematical analysis | Exact solutions

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 11/2019, Volume 78, Issue 10, pp. 3390 - 3407

The extended simplest equation method is employed in this article to construct many solitons and other solutions for two nonlinear partial differential...

Extended quantum ZK equation | Solitons and other solutions | Extended simplest equation method | Modified ZK equation | MATHEMATICS, APPLIED | TANH METHOD | MAPPING METHOD | ZAKHAROV-KUZNETSOV EQUATION | SUB-ODE METHOD | OPTICAL SOLITONS | TRAVELING-WAVE SOLUTIONS | EXP-FUNCTION METHOD | RICCATI EQUATION | NONLINEAR TERMS | KDV-MKDV EQUATION | Magnetic fields | Analysis | Methods | Differential equations | Nonlinear equations | Partial differential equations | Plasma (physics) | Solitary waves | Nonlinear differential equations | Acoustic waves

Extended quantum ZK equation | Solitons and other solutions | Extended simplest equation method | Modified ZK equation | MATHEMATICS, APPLIED | TANH METHOD | MAPPING METHOD | ZAKHAROV-KUZNETSOV EQUATION | SUB-ODE METHOD | OPTICAL SOLITONS | TRAVELING-WAVE SOLUTIONS | EXP-FUNCTION METHOD | RICCATI EQUATION | NONLINEAR TERMS | KDV-MKDV EQUATION | Magnetic fields | Analysis | Methods | Differential equations | Nonlinear equations | Partial differential equations | Plasma (physics) | Solitary waves | Nonlinear differential equations | Acoustic waves

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 7/2018, Volume 93, Issue 2, pp. 733 - 740

A variety of new types of nonautonomous combined multi-wave solutions of the ($$2+1$$ 2+1 )-dimensional variable coefficients KdV equation is derived by means...

Engineering | Vibration, Dynamical Systems, Control | Generalized unified method | Variable coefficients | Classical Mechanics | Automotive Engineering | Mechanical Engineering | ( $$2+1$$ 2 + 1 )-dimensional KdV equation | Combined multi-wave solutions | (2 + 1)-dimensional KdV equation | SYSTEM | RATIONAL SOLUTIONS | (2+1)-dimensional KdV equation | DE-VRIES EQUATION | WAVE SOLUTIONS | MULTIPLE-SOLITON-SOLUTIONS | ENGINEERING, MECHANICAL | KORTEWEG-DEVRIES EQUATION | MULTISOLITON SOLUTIONS | MECHANICS | EVOLUTION | KP EQUATION | Electrical engineering | Solitary waves

Engineering | Vibration, Dynamical Systems, Control | Generalized unified method | Variable coefficients | Classical Mechanics | Automotive Engineering | Mechanical Engineering | ( $$2+1$$ 2 + 1 )-dimensional KdV equation | Combined multi-wave solutions | (2 + 1)-dimensional KdV equation | SYSTEM | RATIONAL SOLUTIONS | (2+1)-dimensional KdV equation | DE-VRIES EQUATION | WAVE SOLUTIONS | MULTIPLE-SOLITON-SOLUTIONS | ENGINEERING, MECHANICAL | KORTEWEG-DEVRIES EQUATION | MULTISOLITON SOLUTIONS | MECHANICS | EVOLUTION | KP EQUATION | Electrical engineering | Solitary waves

Journal Article

Optical and Quantum Electronics, ISSN 0306-8919, 8/2017, Volume 49, Issue 8, pp. 1 - 15

In this paper, the first integral method and the functional variable method are used to establish exact traveling wave solutions of the space–time fractional...

Modified KDV–Zakharov–Kuznetsov equation | Conformable fractional derivative | First integral method | Optics, Lasers, Photonics, Optical Devices | Characterization and Evaluation of Materials | Schrödinger–Hirota equation | Computer Communication Networks | Physics | Functional variable method | Electrical Engineering | QUANTUM SCIENCE & TECHNOLOGY | 1ST INTEGRAL METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | Modified KDV-Zakharov-Kuznetsov equation | WAVE SOLUTIONS | OPTICS | Schrodinger-Hirota equation | ENGINEERING, ELECTRICAL & ELECTRONIC | Differential equations | Aerospace engineering

Modified KDV–Zakharov–Kuznetsov equation | Conformable fractional derivative | First integral method | Optics, Lasers, Photonics, Optical Devices | Characterization and Evaluation of Materials | Schrödinger–Hirota equation | Computer Communication Networks | Physics | Functional variable method | Electrical Engineering | QUANTUM SCIENCE & TECHNOLOGY | 1ST INTEGRAL METHOD | PARTIAL-DIFFERENTIAL-EQUATIONS | Modified KDV-Zakharov-Kuznetsov equation | WAVE SOLUTIONS | OPTICS | Schrodinger-Hirota equation | ENGINEERING, ELECTRICAL & ELECTRONIC | Differential equations | Aerospace engineering

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 9/2016, Volume 85, Issue 4, pp. 2449 - 2465

In this paper, we study the application of a version of the method of simplest equation for obtaining exact traveling wave solutions of the Zakharov–Kuznetsov...

Engineering | Vibration, Dynamical Systems, Control | Modified Zakharov–Kuznetsov equation | Modified method of simplest equation | Exact solutions | Mechanics | Automotive Engineering | Zakharov–Kuznetsov equation | Mechanical Engineering | Zakharov-Kuznetsov equation | 1-SOLITON SOLUTION | DE-VRIES EQUATION | ENGINEERING, MECHANICAL | TRAVELING-WAVE SOLUTIONS | MECHANICS | PARTIAL-DIFFERENTIAL-EQUATIONS | SYMBOLIC COMPUTATION | TIME-DEPENDENT COEFFICIENTS | BOUSSINESQ EQUATIONS | Modified Zakharov-Kuznetsov equation | KDV EQUATION | NONLINEAR EVOLUTION-EQUATIONS | VARIABLE SEPARATION APPROACH | Information science | Methods | Traveling waves | Nonlinear equations | Partial differential equations | Mathematical analysis | Nonlinear differential equations

Engineering | Vibration, Dynamical Systems, Control | Modified Zakharov–Kuznetsov equation | Modified method of simplest equation | Exact solutions | Mechanics | Automotive Engineering | Zakharov–Kuznetsov equation | Mechanical Engineering | Zakharov-Kuznetsov equation | 1-SOLITON SOLUTION | DE-VRIES EQUATION | ENGINEERING, MECHANICAL | TRAVELING-WAVE SOLUTIONS | MECHANICS | PARTIAL-DIFFERENTIAL-EQUATIONS | SYMBOLIC COMPUTATION | TIME-DEPENDENT COEFFICIENTS | BOUSSINESQ EQUATIONS | Modified Zakharov-Kuznetsov equation | KDV EQUATION | NONLINEAR EVOLUTION-EQUATIONS | VARIABLE SEPARATION APPROACH | Information science | Methods | Traveling waves | Nonlinear equations | Partial differential equations | Mathematical analysis | Nonlinear differential equations

Journal Article

7.
Full Text
Interaction behaviors for the ($$\varvec{2+1}$$ 2+1 )-dimensional Sawada–Kotera equation

Nonlinear Dynamics, ISSN 0924-090X, 7/2018, Volume 93, Issue 2, pp. 741 - 747

In this work, in this paper, we mainly study two kinds of interaction solutions of the ($$2+1$$ 2+1 )-dimensional Sawada–Kotera equation, one of which is the...

Gravitational force | Engineering | Vibration, Dynamical Systems, Control | Dynamic | Double exponential function | Classical Mechanics | Trigonometric function | Automotive Engineering | Mechanical Engineering | RATIONAL SOLUTIONS | MECHANICS | KDV EQUATION | WAVE SOLUTIONS | NONLINEAR SCHRODINGER-EQUATION | MULTIPLE-SOLITON-SOLUTIONS | ENGINEERING, MECHANICAL | Trigonometric functions | Exponential functions | Rational functions

Gravitational force | Engineering | Vibration, Dynamical Systems, Control | Dynamic | Double exponential function | Classical Mechanics | Trigonometric function | Automotive Engineering | Mechanical Engineering | RATIONAL SOLUTIONS | MECHANICS | KDV EQUATION | WAVE SOLUTIONS | NONLINEAR SCHRODINGER-EQUATION | MULTIPLE-SOLITON-SOLUTIONS | ENGINEERING, MECHANICAL | Trigonometric functions | Exponential functions | Rational functions

Journal Article

Results in Physics, ISSN 2211-3797, 2015, Volume 5, Issue C, pp. 125 - 130

The modified simple equation (MSE) method is a competent and highly effective mathematical tool for extracting exact traveling wave solutions to nonlinear...

Nonlinear evolution equations | Phi-4 equation | Solitary wave solutions | Benney–Luke equation | Modified simple equation method | Benney-Luke equation | PERTURBATION-THEORY | (G'/G)-EXPANSION METHOD | SOLITONS | PHYSICS, MULTIDISCIPLINARY | MATERIALS SCIENCE, MULTIDISCIPLINARY | EXPANSION | KDV

Nonlinear evolution equations | Phi-4 equation | Solitary wave solutions | Benney–Luke equation | Modified simple equation method | Benney-Luke equation | PERTURBATION-THEORY | (G'/G)-EXPANSION METHOD | SOLITONS | PHYSICS, MULTIDISCIPLINARY | MATERIALS SCIENCE, MULTIDISCIPLINARY | EXPANSION | KDV

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 10/2014, Volume 245, pp. 289 - 304

In the present work, a mathematical model to obtain the solution of the nonlinear wave by coupling the Rosenau–KdV equation and the Rosenau–RLW equation is...

Rosenau–RLW equation | Stability | Rosenau–KdV equation | Finite difference method | Convergence | Rosenau-KdV equation | Rosenau-RLW equation | MATHEMATICS, APPLIED | SOLITONS | NUMERICAL-METHOD

Rosenau–RLW equation | Stability | Rosenau–KdV equation | Finite difference method | Convergence | Rosenau-KdV equation | Rosenau-RLW equation | MATHEMATICS, APPLIED | SOLITONS | NUMERICAL-METHOD

Journal Article

2015, Volume 651.

Conference Proceeding

Nonlinear Dynamics, ISSN 0924-090X, 2/2018, Volume 91, Issue 3, pp. 1619 - 1626

In this paper, we establish a new nonlinear equation which is called the two-mode Korteweg–de Vries–Burgers equation (TMKdV–BE). The new equation describes the...

74J35 | Engineering | Vibration, Dynamical Systems, Control | Two-mode KdV–Burgers equation | Tanh–coth expansion method | Classical Mechanics | Simplified bilinear method | Automotive Engineering | Mechanical Engineering | 35C08 | MATHEMATICAL PHYSICS | MECHANICS | SOLITONS | Two-mode KdV-Burgers equation | SOLITARY WAVE SOLUTIONS | SYSTEMS | Tanh-coth expansion method | KDV EQUATION | EVOLUTION-EQUATIONS | ENGINEERING, MECHANICAL | Series (mathematics) | Nonlinear equations | Wave propagation | Burgers equation

74J35 | Engineering | Vibration, Dynamical Systems, Control | Two-mode KdV–Burgers equation | Tanh–coth expansion method | Classical Mechanics | Simplified bilinear method | Automotive Engineering | Mechanical Engineering | 35C08 | MATHEMATICAL PHYSICS | MECHANICS | SOLITONS | Two-mode KdV-Burgers equation | SOLITARY WAVE SOLUTIONS | SYSTEMS | Tanh-coth expansion method | KDV EQUATION | EVOLUTION-EQUATIONS | ENGINEERING, MECHANICAL | Series (mathematics) | Nonlinear equations | Wave propagation | Burgers equation

Journal Article

Physics Letters A, ISSN 0375-9601, 2006, Volume 356, Issue 2, pp. 119 - 123

A further improved extended Fan sub-equation method is proposed to seek more types of exact solutions of non-linear partial differential equations. Applying...

Triangular-like solutions | Weierstrass elliptic doubly-like periodic solutions | The modified extended Fan sub-equation method | Jacobi elliptic wave function-like solutions | Soliton-like solutions | EXPANSION METHOD | SERIES | PHYSICS, MULTIDISCIPLINARY | soliton-like solutions | KDV-BURGERS EQUATION | VARIANT BOUSSINESQ EQUATIONS | TRAVELING-WAVE SOLUTIONS | MKDV | PARTIAL-DIFFERENTIAL-EQUATIONS | triangular-like solutions | COEFFICIENTS | the modified extended Fan sub-equation method

Triangular-like solutions | Weierstrass elliptic doubly-like periodic solutions | The modified extended Fan sub-equation method | Jacobi elliptic wave function-like solutions | Soliton-like solutions | EXPANSION METHOD | SERIES | PHYSICS, MULTIDISCIPLINARY | soliton-like solutions | KDV-BURGERS EQUATION | VARIANT BOUSSINESQ EQUATIONS | TRAVELING-WAVE SOLUTIONS | MKDV | PARTIAL-DIFFERENTIAL-EQUATIONS | triangular-like solutions | COEFFICIENTS | the modified extended Fan sub-equation method

Journal Article

Pramana, ISSN 0304-4289, 8/2013, Volume 81, Issue 2, pp. 203 - 214

In this paper, we obtain the 1-soliton solutions of the (3 + 1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation and the generalized Benjamin...

Astrophysics and Astroparticles | Exact solutions | (3 + 1)-dimensional generalized Kadomtsev–Petviashvili equation | the generalized Benjamin equation | dark soliton | Physics, general | bright soliton | Physics | Astronomy, Observations and Techniques | Bright soliton | (3 + 1)-dimensional generalized Kadomtsev- Petviashvili equation | Dark soliton | The generalized Benjamin equation | LAW | TANH METHOD | PHYSICS, MULTIDISCIPLINARY | F-EXPANSION METHOD | NONLINEAR EVOLUTION | OPTICAL SOLITONS | (3+1)-dimensional generalized Kadomtsev-Petviashvili equation | (G'/G)-EXPANSION METHOD | TRAVELING-WAVE SOLUTIONS | EXP-FUNCTION METHOD | MEDIA | KDV

Astrophysics and Astroparticles | Exact solutions | (3 + 1)-dimensional generalized Kadomtsev–Petviashvili equation | the generalized Benjamin equation | dark soliton | Physics, general | bright soliton | Physics | Astronomy, Observations and Techniques | Bright soliton | (3 + 1)-dimensional generalized Kadomtsev- Petviashvili equation | Dark soliton | The generalized Benjamin equation | LAW | TANH METHOD | PHYSICS, MULTIDISCIPLINARY | F-EXPANSION METHOD | NONLINEAR EVOLUTION | OPTICAL SOLITONS | (3+1)-dimensional generalized Kadomtsev-Petviashvili equation | (G'/G)-EXPANSION METHOD | TRAVELING-WAVE SOLUTIONS | EXP-FUNCTION METHOD | MEDIA | KDV

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 1/2017, Volume 87, Issue 2, pp. 1209 - 1216

In this paper, the generalized unified method is used to construct multi-rational wave solutions of the ( $$2 + 1$$ 2 + 1 )-dimensional Kadomtsev–Petviashvili...

Engineering | Vibration, Dynamical Systems, Control | The generalized unified method | Multi-rational solutions | Variable coefficients | Classical Mechanics | The ( 2 $$+$$ + 1)-dimensional Kadomtsev–Petviashvili equation | Automotive Engineering | Mechanical Engineering | The (2 + 1)-dimensional Kadomtsev–Petviashvili equation | MECHANICS | KP EQUATION | SYMBOLIC COMPUTATION | The (2+1)-dimensional Kadomtsev-Petviashvili equation | KDV EQUATION | ENGINEERING, MECHANICAL | Fluid dynamics | Plasma physics | Nonlinear phenomena | Coefficients | Plasma (physics) | Solitary waves

Engineering | Vibration, Dynamical Systems, Control | The generalized unified method | Multi-rational solutions | Variable coefficients | Classical Mechanics | The ( 2 $$+$$ + 1)-dimensional Kadomtsev–Petviashvili equation | Automotive Engineering | Mechanical Engineering | The (2 + 1)-dimensional Kadomtsev–Petviashvili equation | MECHANICS | KP EQUATION | SYMBOLIC COMPUTATION | The (2+1)-dimensional Kadomtsev-Petviashvili equation | KDV EQUATION | ENGINEERING, MECHANICAL | Fluid dynamics | Plasma physics | Nonlinear phenomena | Coefficients | Plasma (physics) | Solitary waves

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 01/2018, Volume 41, Issue 1, pp. 80 - 87

In this work, we develop a new integrable equation by combining the KdV equation and the negative‐order KdV equation. We use concurrently the KdV recursion...

KdV equation | Painlevé analysis | recursion operator | multiple soliton solutions | negative‐order KdV equation | negative-order KdV equation | MULTIPLE SOLITON | MATHEMATICS, APPLIED | RECURSION OPERATORS | Painleve analysis

KdV equation | Painlevé analysis | recursion operator | multiple soliton solutions | negative‐order KdV equation | negative-order KdV equation | MULTIPLE SOLITON | MATHEMATICS, APPLIED | RECURSION OPERATORS | Painleve analysis

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 11/2013, Volume 224, pp. 517 - 523

In this paper, we successfully construct the new exact traveling wave solutions of the coupled Schrödinger–Boussinesq equation by using the extended simplest...

The coupled Schrödinger–Boussinesq equation | The extended simplest equation method | The traveling wave solutions | The coupled Schrödinger-Boussinesq equation | SYSTEM | NONLINEAR DIFFERENTIAL-EQUATIONS | MATHEMATICS, APPLIED | TRAVELING-WAVE SOLUTIONS | EXPANSION | KDV EQUATION | EVOLUTION-EQUATIONS | The coupled Schrodinger-Boussinesq equation | PLASMAS

The coupled Schrödinger–Boussinesq equation | The extended simplest equation method | The traveling wave solutions | The coupled Schrödinger-Boussinesq equation | SYSTEM | NONLINEAR DIFFERENTIAL-EQUATIONS | MATHEMATICS, APPLIED | TRAVELING-WAVE SOLUTIONS | EXPANSION | KDV EQUATION | EVOLUTION-EQUATIONS | The coupled Schrodinger-Boussinesq equation | PLASMAS

Journal Article

Chaos, Solitons and Fractals, ISSN 0960-0779, 2009, Volume 42, Issue 3, pp. 1356 - 1363

A direct approach to exact solutions of nonlinear partial differential equations is proposed, by using rational function transformations. The new method...

PHYSICS, MULTIDISCIPLINARY | DAVEY-STEWARTSON EQUATION | MAPPING METHOD | F-EXPANSION METHOD | DE-VRIES EQUATION | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SOLITARY-WAVE SOLUTIONS | EXP-FUNCTION METHOD | WRONSKIAN SOLUTIONS | NONLINEAR EVOLUTION-EQUATIONS | GENERALIZED KDV EQUATION | TANH-FUNCTION METHOD

PHYSICS, MULTIDISCIPLINARY | DAVEY-STEWARTSON EQUATION | MAPPING METHOD | F-EXPANSION METHOD | DE-VRIES EQUATION | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SOLITARY-WAVE SOLUTIONS | EXP-FUNCTION METHOD | WRONSKIAN SOLUTIONS | NONLINEAR EVOLUTION-EQUATIONS | GENERALIZED KDV EQUATION | TANH-FUNCTION METHOD

Journal Article

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

2001, Lecture notes in mathematics, ISBN 3540418334, Volume 1756, 146

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