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

Physics Reports, ISSN 0370-1573, 02/2013, Volume 523, Issue 2, pp. 61 - 126

In the past years there was a huge interest in experimental and theoretical studies in the area of few-optical-cycle pulses and in the broader fast growing...

Few-cycle dissipative solitons | Generalized Kadomtsev–Petviashvili equation | Two-level atoms | Circular polarization | Maxwell–Bloch equations | Few-optical-cycle solitons | Modified Korteweg–de Vries equation | Density matrix | Long-wave approximation | Few-cycle pulses | Reductive perturbation method | Half-cycle optical solitons | Short-wave approximation | Unipolar pulses | Few-cycle light bullets | Linear polarization | Sine–Gordon equation | Complex modified Korteweg–de Vries equation | Modified Korteweg-de Vries equation | Generalized Kadomtsev-Petviashvili equation | Complex modified Korteweg-de Vries equation | Sine-Gordon equation | Maxwell-Bloch equations | ULTRA-SHORT PULSES | SELF-INDUCED TRANSPARENCY | SOLITARY-WAVE SOLUTIONS | QUADRATIC NONLINEAR MEDIA | PHYSICS, MULTIDISCIPLINARY | DE-VRIES EQUATION | KADOMTSEV-PETVIASHVILI EQUATION | SINE-GORDON EQUATIONS | TI-SAPPHIRE LASER | SHORT ELECTROMAGNETIC PULSES | SHORT-PULSE EQUATION | Analysis | Models | Wave propagation

Few-cycle dissipative solitons | Generalized Kadomtsev–Petviashvili equation | Two-level atoms | Circular polarization | Maxwell–Bloch equations | Few-optical-cycle solitons | Modified Korteweg–de Vries equation | Density matrix | Long-wave approximation | Few-cycle pulses | Reductive perturbation method | Half-cycle optical solitons | Short-wave approximation | Unipolar pulses | Few-cycle light bullets | Linear polarization | Sine–Gordon equation | Complex modified Korteweg–de Vries equation | Modified Korteweg-de Vries equation | Generalized Kadomtsev-Petviashvili equation | Complex modified Korteweg-de Vries equation | Sine-Gordon equation | Maxwell-Bloch equations | ULTRA-SHORT PULSES | SELF-INDUCED TRANSPARENCY | SOLITARY-WAVE SOLUTIONS | QUADRATIC NONLINEAR MEDIA | PHYSICS, MULTIDISCIPLINARY | DE-VRIES EQUATION | KADOMTSEV-PETVIASHVILI EQUATION | SINE-GORDON EQUATIONS | TI-SAPPHIRE LASER | SHORT ELECTROMAGNETIC PULSES | SHORT-PULSE EQUATION | Analysis | Models | Wave propagation

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

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

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

Book

Computers and Mathematics with Applications, ISSN 0898-1221, 09/2017, Volume 74, Issue 6, pp. 1399 - 1405

By using the Hirota bilinear form of the KP equation, twelve classes of lump–kink solutions are presented under the help of symbolic computations with Maple....

Soliton solution | Bilinear form | Lump solution | RATIONAL SOLUTIONS | MATHEMATICS, APPLIED | BELL POLYNOMIALS | LATTICE EQUATION | DE-VRIES EQUATION | RESONANT SOLUTIONS | KADOMTSEV-PETVIASHVILI EQUATION | SOLITON-SOLUTIONS | SYMMETRY CONSTRAINT | BILINEAR EQUATIONS | KORTEWEG-DEVRIES

Soliton solution | Bilinear form | Lump solution | RATIONAL SOLUTIONS | MATHEMATICS, APPLIED | BELL POLYNOMIALS | LATTICE EQUATION | DE-VRIES EQUATION | RESONANT SOLUTIONS | KADOMTSEV-PETVIASHVILI EQUATION | SOLITON-SOLUTIONS | SYMMETRY CONSTRAINT | BILINEAR EQUATIONS | KORTEWEG-DEVRIES

Journal Article

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

Book

Results in Physics, ISSN 2211-3797, 2017, Volume 7, pp. 1143 - 1149

The Boussinesq equation with dual dispersion and modified Korteweg–de Vries–Kadomtsev–Petviashvili equations describe weakly dispersive and small amplitude...

Modified Korteweg–de Vries–Kadomtsev–Petviashvili equation | Breaking soliton equation | Boussinesq equation

Modified Korteweg–de Vries–Kadomtsev–Petviashvili equation | Breaking soliton equation | Boussinesq equation

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 07/2017, Volume 89, Issue 1, pp. 235 - 241

In this paper, a modified KdV-CBS equation is investigated by using the truncated Painleve expansion and consistent Riccati expansion method, respectively. It...

Nonlocal symmetry | Soliton–cnoidal solution | Consistent Riccati expansion | WAVE INTERACTION SOLUTION | INTEGRABLE MODELS | MECHANICS | Soliton-cnoidal solution | DE-VRIES EQUATION | ENGINEERING, MECHANICAL | INVERSE SPECTRAL TRANSFORM | Art schools | Cnoidal waves | Wave interaction | Solitary waves | Symmetry

Nonlocal symmetry | Soliton–cnoidal solution | Consistent Riccati expansion | WAVE INTERACTION SOLUTION | INTEGRABLE MODELS | MECHANICS | Soliton-cnoidal solution | DE-VRIES EQUATION | ENGINEERING, MECHANICAL | INVERSE SPECTRAL TRANSFORM | Art schools | Cnoidal waves | Wave interaction | Solitary waves | Symmetry

Journal Article

1990, Pitman monographs and surveys in pure and applied mathematics, ISBN 9780470214176, Volume 49, xvii, 417 p. --

Book

Computers and Mathematics with Applications, ISSN 0898-1221, 04/2019, Volume 77, Issue 8, pp. 2255 - 2262

In this article, via the improved fractional subequation method, the fully analytical solutions of the (2+1)-dimensional space–time fractional Burgers equation...

(2+1)-dimensional Korteweg–de Vries equation | Improved fractional sub-equation method | Modified Riemann–Liouville derivative | (2+1)-dimensional Burgers equation | TRANSFORMATION | ORDER | MATHEMATICS, APPLIED | CALCULUS | Modified Riemann-Liouville derivative | DIFFERENTIAL-EQUATIONS | (2+1)-dimensional Korteweg-de Vries equation | Graphical representations | Linear equations | Burgers equation | Solitary waves | Exact solutions

(2+1)-dimensional Korteweg–de Vries equation | Improved fractional sub-equation method | Modified Riemann–Liouville derivative | (2+1)-dimensional Burgers equation | TRANSFORMATION | ORDER | MATHEMATICS, APPLIED | CALCULUS | Modified Riemann-Liouville derivative | DIFFERENTIAL-EQUATIONS | (2+1)-dimensional Korteweg-de Vries equation | Graphical representations | Linear equations | Burgers equation | Solitary waves | Exact solutions

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

2011, ISBN 9789814360739, xiv, 283

Book

Applied Mathematics and Computation, ISSN 0096-3003, 2007, Volume 187, Issue 2, pp. 1368 - 1372

With the help of the symbolic computation system Maple, we present Korteweg–de Vries equation-based sub-equation method. Being concise and straightforward, it...

(2 + 1)-dimensional Korteweg–de Vries equation | Korteweg–de Vries equation-based sub-equation method | Nonlinear partial differential equations | N-soliton solution | (2 + 1)-dimensional Korteweg-de Vries equation | Korteweg-de Vries equation-based sub-equation method | MATHEMATICS, APPLIED | BREAKING SOLITON EQUATION | EXPLICIT EXACT-SOLUTIONS | DIFFERENTIAL-EQUATIONS | RATIONAL EXPANSION METHOD | PERIODIC-WAVE SOLUTIONS | HOMOGENEOUS BALANCE METHOD | nonlinear partial differential equations | SYMBOLIC COMPUTATION | BURGERS-EQUATION | NONLINEAR EVOLUTION-EQUATIONS | TANH-FUNCTION METHOD | (2+1)-dimensional Korteweg-de Vries equation

(2 + 1)-dimensional Korteweg–de Vries equation | Korteweg–de Vries equation-based sub-equation method | Nonlinear partial differential equations | N-soliton solution | (2 + 1)-dimensional Korteweg-de Vries equation | Korteweg-de Vries equation-based sub-equation method | MATHEMATICS, APPLIED | BREAKING SOLITON EQUATION | EXPLICIT EXACT-SOLUTIONS | DIFFERENTIAL-EQUATIONS | RATIONAL EXPANSION METHOD | PERIODIC-WAVE SOLUTIONS | HOMOGENEOUS BALANCE METHOD | nonlinear partial differential equations | SYMBOLIC COMPUTATION | BURGERS-EQUATION | NONLINEAR EVOLUTION-EQUATIONS | TANH-FUNCTION METHOD | (2+1)-dimensional Korteweg-de Vries equation

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 10/2010, Volume 15, Issue 10, pp. 2778 - 2790

Exact solutions of some popular nonlinear ordinary differential equations are analyzed taking their Laurent series into account. Using the Laurent series for...

Kuramoto–Sivashinsky equation | Laurent series | Korteweg–de Vries equation | Nonlinear ordinary differential equation | Kawahara equation | Riccati equation | Burgers equation | Exp-function method | Exact solution | Meromorphic solution | Korteweg-de Vries equation | Kuramoto-Sivashinsky equation | EXPANSION METHOD | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | OSTROVSKY EQUATION | NONINTEGRABLE EQUATIONS | PHYSICS, MATHEMATICAL | TRAVELING-WAVE SOLUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | EVOLUTION EQUATION | SYMBOLIC COMPUTATION | KDV-BURGERS EQUATIONS | FISHER EQUATION | Differential equations | Nonlinearity | Mathematical models | Computer simulation | Mathematical analysis | Exact solutions | Physics - Exactly Solvable and Integrable Systems

Kuramoto–Sivashinsky equation | Laurent series | Korteweg–de Vries equation | Nonlinear ordinary differential equation | Kawahara equation | Riccati equation | Burgers equation | Exp-function method | Exact solution | Meromorphic solution | Korteweg-de Vries equation | Kuramoto-Sivashinsky equation | EXPANSION METHOD | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | OSTROVSKY EQUATION | NONINTEGRABLE EQUATIONS | PHYSICS, MATHEMATICAL | TRAVELING-WAVE SOLUTIONS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | EVOLUTION EQUATION | SYMBOLIC COMPUTATION | KDV-BURGERS EQUATIONS | FISHER EQUATION | Differential equations | Nonlinearity | Mathematical models | Computer simulation | Mathematical analysis | Exact solutions | Physics - Exactly Solvable and Integrable Systems

Journal Article

2015, Volume 635

Conference Proceeding

Nonlinear Dynamics, ISSN 0924-090X, 3/2017, Volume 87, Issue 4, pp. 2661 - 2676

In this paper, the Riemann–Bäcklund method is extended to a generalized variable coefficient ( $$2+1$$ 2 + 1 )-dimensional Korteweg–de Vries equation. The...

Engineering | Vibration, Dynamical Systems, Control | 34C25 | Quasiperiodic wave solutions | Classical Mechanics | Bäcklund transformation | Automotive Engineering | 35Q53 | Mechanical Engineering | A generalized variable coefficient ( $$2+1$$ 2 + 1 )-dimensional Korteweg–de Vries equation | Soliton solutions | 37K40 | A generalized variable coefficient (2 + 1)-dimensional Korteweg–de Vries equation | TRANSFORMATION | SYSTEM | MECHANICS | A generalized variable coefficient (2+1)-dimensional Korteweg-de Vries equation | BREATHERS | Backlund transformation | EVOLUTION-EQUATIONS | ENGINEERING, MECHANICAL | SOLITON | Solitary waves | Wave propagation

Engineering | Vibration, Dynamical Systems, Control | 34C25 | Quasiperiodic wave solutions | Classical Mechanics | Bäcklund transformation | Automotive Engineering | 35Q53 | Mechanical Engineering | A generalized variable coefficient ( $$2+1$$ 2 + 1 )-dimensional Korteweg–de Vries equation | Soliton solutions | 37K40 | A generalized variable coefficient (2 + 1)-dimensional Korteweg–de Vries equation | TRANSFORMATION | SYSTEM | MECHANICS | A generalized variable coefficient (2+1)-dimensional Korteweg-de Vries equation | BREATHERS | Backlund transformation | EVOLUTION-EQUATIONS | ENGINEERING, MECHANICAL | SOLITON | Solitary waves | Wave propagation

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