1.
Evolution equations of hyperbolic and Schrödinger type

: asymptotics, estimates and nonlinearities

2012, 1. Aufl., Progress in mathematics, ISBN 9783034804530, Volume 301, viii, 324

Evolution equations of hyperbolic or more general p-evolution type form an active field of current research. This volume aims to collect some recent advances...

Differential equations, Hyperbolic | Schrödinger equation | Evolution equations | Schrodinger equation

Differential equations, Hyperbolic | Schrödinger equation | Evolution equations | Schrodinger equation

Book

2011, ISBN 9789814360739, xiv, 283

Book

Pramana - Journal of Physics, ISSN 0304-4289, 05/2018, Volume 90, Issue 5, p. 1

In this research, we apply two different techniques on nonlinear complex fractional nonlinear Schrodinger equation which is a very important model in...

new auxiliary equation method | novel (G | G) -expansion method | optical solitary travelling wave solutions | Nonlinear complex fractional Schrödinger equation | kink and antikink | BOUSSINESQ EQUATION | PHYSICS, MULTIDISCIPLINARY | BIFURCATIONS | novel (G '/G)-expansion method | FIBERS | TRAVELING-WAVE SOLUTIONS | EVOLUTION | Nonlinear complex fractional Schrodinger equation | GINZBURG-LANDAU EQUATION | BRIGHT | Quantum theory | Methods

new auxiliary equation method | novel (G | G) -expansion method | optical solitary travelling wave solutions | Nonlinear complex fractional Schrödinger equation | kink and antikink | BOUSSINESQ EQUATION | PHYSICS, MULTIDISCIPLINARY | BIFURCATIONS | novel (G '/G)-expansion method | FIBERS | TRAVELING-WAVE SOLUTIONS | EVOLUTION | Nonlinear complex fractional Schrodinger equation | GINZBURG-LANDAU EQUATION | BRIGHT | Quantum theory | Methods

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 6/2016, Volume 84, Issue 4, pp. 1883 - 1900

This paper addresses the Biswas–Milovic equation as a generalized model for soliton propagation through optical wave guides. The extended trail equation method...

Engineering | Vibration, Dynamical Systems, Control | Biswas–Milovic equation | Integrability | Optical solitons | Extended trail equation method | Mechanics | Automotive Engineering | Mechanical Engineering | DISPERSION | CLASSIFICATION | NONLINEAR SCHRODINGERS EQUATION | ENGINEERING, MECHANICAL | POWER-LAW | PERTURBATION-THEORY | TRAVELING-WAVE SOLUTIONS | MECHANICS | SINGULAR SOLITONS | KERR | MEDIA | TOPOLOGICAL 1-SOLITON SOLUTION | Biswas-Milovic equation | Waveguides | Analysis | Methods | Algorithms | Wave propagation | Solitary waves | Nonlinear dynamics | Mathematical analysis | Solitons | Byproducts | Mathematical models

Engineering | Vibration, Dynamical Systems, Control | Biswas–Milovic equation | Integrability | Optical solitons | Extended trail equation method | Mechanics | Automotive Engineering | Mechanical Engineering | DISPERSION | CLASSIFICATION | NONLINEAR SCHRODINGERS EQUATION | ENGINEERING, MECHANICAL | POWER-LAW | PERTURBATION-THEORY | TRAVELING-WAVE SOLUTIONS | MECHANICS | SINGULAR SOLITONS | KERR | MEDIA | TOPOLOGICAL 1-SOLITON SOLUTION | Biswas-Milovic equation | Waveguides | Analysis | Methods | Algorithms | Wave propagation | Solitary waves | Nonlinear dynamics | Mathematical analysis | Solitons | Byproducts | Mathematical models

Journal Article

Physics Letters A, ISSN 0375-9601, 2008, Volume 372, Issue 4, pp. 417 - 423

The ( G ′ G )-expansion method is firstly proposed, where G = G ( ξ ) satisfies a second order linear ordinary differential equation (LODE for short), by which...

Travelling wave solutions | Hirota–Satsuma equations | KdV equation | Variant Boussinesq equations | ( [formula omitted])-expansion method | Homogeneous balance | Solitary wave solutions | mKdV equation | Hirota-Satsuma equations | G))-expansion method | frac(G | EXPANSION METHOD | F-EXPANSION | NONCOMPACT STRUCTURES | VARIANTS | PHYSICS, MULTIDISCIPLINARY | SCHRODINGER-EQUATION | SUB-ODE METHOD | (G '/G)-expansion method | PARTIAL-DIFFERENTIAL-EQUATIONS | solitary wave solutions | homogeneous balance | travelling wave solutions | variant Boussinesq equations | EXPLICIT

Travelling wave solutions | Hirota–Satsuma equations | KdV equation | Variant Boussinesq equations | ( [formula omitted])-expansion method | Homogeneous balance | Solitary wave solutions | mKdV equation | Hirota-Satsuma equations | G))-expansion method | frac(G | EXPANSION METHOD | F-EXPANSION | NONCOMPACT STRUCTURES | VARIANTS | PHYSICS, MULTIDISCIPLINARY | SCHRODINGER-EQUATION | SUB-ODE METHOD | (G '/G)-expansion method | PARTIAL-DIFFERENTIAL-EQUATIONS | solitary wave solutions | homogeneous balance | travelling wave solutions | variant Boussinesq equations | EXPLICIT

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

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

Physics Letters A, ISSN 0375-9601, 06/2017, Volume 381, Issue 21, pp. 1791 - 1794

We present nonlocal integrable reductions of the Fordy–Kulish system of nonlinear Schrodinger equations and the Fordy system of derivative nonlinear...

Nonlocal integrable equations | Nonlinear Schrodinger equations | Fordy–Kulish system | PHYSICS, MULTIDISCIPLINARY | NONLINEAR SCHRODINGER-EQUATION | Fordy-Kulish system | Physics - Exactly Solvable and Integrable Systems

Nonlocal integrable equations | Nonlinear Schrodinger equations | Fordy–Kulish system | PHYSICS, MULTIDISCIPLINARY | NONLINEAR SCHRODINGER-EQUATION | Fordy-Kulish system | Physics - Exactly Solvable and Integrable Systems

Journal Article

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

Optical and Quantum Electronics, ISSN 0306-8919, 3/2018, Volume 50, Issue 3, pp. 1 - 12

This study constructs bright and singular optical solitons the ($$2+1$$ 2+1 )-dimensional NLSE and the Hirota equation by utilizing the new sine-Gordon...

The new SGEM | NLSE | Optics, Lasers, Photonics, Optical Devices | Characterization and Evaluation of Materials | Hirota equation | Computer Communication Networks | Physics | Electrical Engineering | Optical soliton | SYSTEM | QUANTUM SCIENCE & TECHNOLOGY | DYNAMICAL EQUATION | BURGERS EQUATION | SOLITARY | DARK | NONLINEAR SCHRODINGER-EQUATION | ENGINEERING, ELECTRICAL & ELECTRONIC | TRAVELING-WAVE SOLUTIONS | 1ST INTEGRAL METHOD | HIGHER-ORDER | OPTICS | POWER-LAW NONLINEARITY

The new SGEM | NLSE | Optics, Lasers, Photonics, Optical Devices | Characterization and Evaluation of Materials | Hirota equation | Computer Communication Networks | Physics | Electrical Engineering | Optical soliton | SYSTEM | QUANTUM SCIENCE & TECHNOLOGY | DYNAMICAL EQUATION | BURGERS EQUATION | SOLITARY | DARK | NONLINEAR SCHRODINGER-EQUATION | ENGINEERING, ELECTRICAL & ELECTRONIC | TRAVELING-WAVE SOLUTIONS | 1ST INTEGRAL METHOD | HIGHER-ORDER | OPTICS | POWER-LAW NONLINEARITY

Journal Article

NONLINEAR DYNAMICS, ISSN 0924-090X, 09/2019, Volume 97, Issue 4, pp. 2829 - 2841

General rational and semi-rational solutions of the modified Kadomtsev-Petviashvili (mKP) equation and the Konopelchenko-Dubrovsky equation are obtained based...

ZERO | Semi-rational solutions | (2+1)-Dimensional Konopelchenko-Dubrovsky equation | WAVE SOLUTIONS | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | ENGINEERING, MECHANICAL | Modified Kadomtsev-Petviashvili equation | MECHANICS | Rational solutions | DYNAMICS | GENERAL SOLITON-SOLUTIONS | KP hierarchy reduction method | TRANSFORMATIONS | Control engineering

ZERO | Semi-rational solutions | (2+1)-Dimensional Konopelchenko-Dubrovsky equation | WAVE SOLUTIONS | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | ENGINEERING, MECHANICAL | Modified Kadomtsev-Petviashvili equation | MECHANICS | Rational solutions | DYNAMICS | GENERAL SOLITON-SOLUTIONS | KP hierarchy reduction method | TRANSFORMATIONS | Control engineering

Journal Article

Optik - International Journal for Light and Electron Optics, ISSN 0030-4026, 07/2017, Volume 140, pp. 136 - 144

•Unstable nonlinear Schrödinger equation is considered.•Extended simple equation method is discussed.•Bright-Dark Solitary wave solutions and solitons are...

Solitary wave solutions | Simple equation method | Unstable nonlinear Schrödinger equation | Solitons | Modify unstable nonlinear Schrödinger equation | SOLITON-SOLUTIONS | equation | Modify unstable nonlinear Schrodinger | Unstable nonlinear Schrodinger equation | OPTICS

Solitary wave solutions | Simple equation method | Unstable nonlinear Schrödinger equation | Solitons | Modify unstable nonlinear Schrödinger equation | SOLITON-SOLUTIONS | equation | Modify unstable nonlinear Schrodinger | Unstable nonlinear Schrodinger equation | OPTICS

Journal Article

13.
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

Computer Physics Communications, ISSN 0010-4655, 01/2019, Volume 234, pp. 55 - 71

We compare the practical performance of adaptive splitting methods for the solution of nonlinear Schrödinger equations. Different methods for local error...

Splitting methods | Embedded methods | Nonlinear Schrödinger equations | Adaptive step-size selection | Local error estimators | Defect-based methods | NUMERICAL-METHODS | PITAEVSKII EQUATIONS | CONVERGENCE ANALYSIS | ACCURATE | PHYSICS, MATHEMATICAL | Nonlinear Schrodinger equations | HERMITE-PSEUDOSPECTRAL-METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | NONUNIFORM FFT | DYNAMICS | CONSERVATION-LAWS | SCHEMES

Splitting methods | Embedded methods | Nonlinear Schrödinger equations | Adaptive step-size selection | Local error estimators | Defect-based methods | NUMERICAL-METHODS | PITAEVSKII EQUATIONS | CONVERGENCE ANALYSIS | ACCURATE | PHYSICS, MATHEMATICAL | Nonlinear Schrodinger equations | HERMITE-PSEUDOSPECTRAL-METHOD | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | NAVIER-STOKES EQUATIONS | NONUNIFORM FFT | DYNAMICS | CONSERVATION-LAWS | SCHEMES

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2010, Volume 217, Issue 1, pp. 1 - 10

In this article, we construct the traveling wave solutions involving parameters of nonlinear evolution equations, via, the perturbed nonlinear Schrödinger...

The modified [formula omitted]-expansion method | The nonlinear cubic–quintic Ginzburg Landau equation | Traveling wave solutions | The perturbed nonlinear Schrödinger equation | The nonlinear cubic-quintic Ginzburg Landau equation | The modified (G′/G)-expansion method | EXPANSION METHOD | MATHEMATICS, APPLIED | MKDV EQUATION | F-EXPANSION | The perturbed nonlinear Schrodinger equation | EXP-FUNCTION METHOD | SUB-ODE METHOD | TANH-FUNCTION METHOD | The modified (G '/G)-expansion method

The modified [formula omitted]-expansion method | The nonlinear cubic–quintic Ginzburg Landau equation | Traveling wave solutions | The perturbed nonlinear Schrödinger equation | The nonlinear cubic-quintic Ginzburg Landau equation | The modified (G′/G)-expansion method | EXPANSION METHOD | MATHEMATICS, APPLIED | MKDV EQUATION | F-EXPANSION | The perturbed nonlinear Schrodinger equation | EXP-FUNCTION METHOD | SUB-ODE METHOD | TANH-FUNCTION METHOD | The modified (G '/G)-expansion method

Journal Article

Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 07/2015, Volume 25, Issue 8, pp. 1447 - 1476

We investigate a class of nonlinear Schrodinger equations with a generalized Choquard nonlinearity and fractional diffusion. We obtain regularity, existence,...

existence | multiplicity | nonexistence | Fractional Laplacian | Choquard equation | BOSON STARS | SCHRODINGER-EQUATIONS | MATHEMATICS, APPLIED | SCALAR FIELD-EQUATIONS | NONLINEARITIES | UNIQUENESS | LAPLACIAN | WAVES | DYNAMICS

existence | multiplicity | nonexistence | Fractional Laplacian | Choquard equation | BOSON STARS | SCHRODINGER-EQUATIONS | MATHEMATICS, APPLIED | SCALAR FIELD-EQUATIONS | NONLINEARITIES | UNIQUENESS | LAPLACIAN | WAVES | DYNAMICS

Journal Article

2012, Volume 581.

Conference Proceeding

Journal of Differential Equations, ISSN 0022-0396, 10/2017, Volume 263, Issue 7, pp. 3943 - 3988

In this paper we study the semiclassical limit for the singularly perturbed Choquard equation−ε2Δu+V(x)u=εμ−3(∫R3Q(y)G(u(y))|x−y|μdy)Q(x)g(u)in R3, where...

Hardy–Littlewood–Sobolev inequality | Critical growth | Choquard equation | Semi-classical solutions | EXISTENCE | NONLINEAR SCHRODINGER-EQUATIONS | MULTIPLICITY | Hardy-Littlewood-Sobolev inequality | POSITIVE SOLUTIONS | SEMICLASSICAL STATES | STANDING WAVES | GROUND-STATE SOLUTIONS | MATHEMATICS | ELLIPTIC PROBLEMS | BOUND-STATES

Hardy–Littlewood–Sobolev inequality | Critical growth | Choquard equation | Semi-classical solutions | EXISTENCE | NONLINEAR SCHRODINGER-EQUATIONS | MULTIPLICITY | Hardy-Littlewood-Sobolev inequality | POSITIVE SOLUTIONS | SEMICLASSICAL STATES | STANDING WAVES | GROUND-STATE SOLUTIONS | MATHEMATICS | ELLIPTIC PROBLEMS | BOUND-STATES

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