Modern Physics Letters B, ISSN 0217-9849, 10/2017, Volume 31, Issue 29, p. 1750269

High-order rogue wave solutions of the Benjamin–Ono equation and the nonlocal nonlinear...

Bilinear method | Rogue waves | Benjamin-Ono equation | Nonlocal nonlinear Schrödinger equation | nonlocal nonlinear Schrodinger equation | RATIONAL SOLUTIONS | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | SOLITON-SOLUTIONS | NLS | DYNAMICS | rogue waves | bilinear method | PHYSICS, MATHEMATICAL

Bilinear method | Rogue waves | Benjamin-Ono equation | Nonlocal nonlinear Schrödinger equation | nonlocal nonlinear Schrodinger equation | RATIONAL SOLUTIONS | PHYSICS, CONDENSED MATTER | PHYSICS, APPLIED | SOLITON-SOLUTIONS | NLS | DYNAMICS | rogue waves | bilinear method | PHYSICS, MATHEMATICAL

Journal Article

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Spatiotemporal dynamics of lump solution to the (1 + 1)-dimensional Benjamin–Ono equation

Nonlinear Dynamics, ISSN 0924-090X, 9/2017, Volume 89, Issue 4, pp. 2723 - 2728

...–Ono equation. Spatiotemporal dynamics of lump solution is investigated and discussed by choice of some parameters $$u_{0}, \beta ,$$ u 0 , β , and $$\gamma $$ γ...

Engineering | Vibration, Dynamical Systems, Control | Benjamin–Ono equation | Classical Mechanics | Spatiotemporal structure | Hirota’s bilinear method | Automotive Engineering | Mechanical Engineering | Lump solution | Parameter perturbation | FLUIDS | WAVE | BOUSSINESQ EQUATION | MECHANICS | Benjamin-Ono equation | EVOLUTION | Hirota's bilinear method | ENGINEERING, MECHANICAL | Extreme value theory | Parameters | Perturbation methods | Solitary waves | Test procedures | Extreme values

Engineering | Vibration, Dynamical Systems, Control | Benjamin–Ono equation | Classical Mechanics | Spatiotemporal structure | Hirota’s bilinear method | Automotive Engineering | Mechanical Engineering | Lump solution | Parameter perturbation | FLUIDS | WAVE | BOUSSINESQ EQUATION | MECHANICS | Benjamin-Ono equation | EVOLUTION | Hirota's bilinear method | ENGINEERING, MECHANICAL | Extreme value theory | Parameters | Perturbation methods | Solitary waves | Test procedures | Extreme values

Journal Article

Forum Mathematicum, ISSN 0933-7741, 01/2020, Volume 32, Issue 1, pp. 151 - 187

In this paper, the well-posedness of the higher-order Benjamin–Ono equation is considered...

35E15 | 35Q53 | modified energy | higher-order Benjamin–Ono equation | Well-posedness | higher-order intermediate long wave equation | MATHEMATICS | MATHEMATICS, APPLIED | SOLITARY WAVES | BEHAVIOR | higher-order Benjamin-Ono equation | CAUCHY-PROBLEM

35E15 | 35Q53 | modified energy | higher-order Benjamin–Ono equation | Well-posedness | higher-order intermediate long wave equation | MATHEMATICS | MATHEMATICS, APPLIED | SOLITARY WAVES | BEHAVIOR | higher-order Benjamin-Ono equation | CAUCHY-PROBLEM

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 10/2016, Volume 333, pp. 185 - 199

Using exact formulae for the scattering data of the Benjamin–Ono equation valid for general rational potentials recently obtained in Miller and Wetzel [17...

Benjamin–Ono equation | Inverse-scattering transform | Small-dispersion limit | KORTEWEG-DEVRIES EQUATION | FLUIDS | UNIVERSALITY | MATHEMATICS, APPLIED | Benjamin-Ono equation | PHYSICS, MULTIDISCIPLINARY | INTERNAL WAVES | PHYSICS, MATHEMATICAL | MODULATION

Benjamin–Ono equation | Inverse-scattering transform | Small-dispersion limit | KORTEWEG-DEVRIES EQUATION | FLUIDS | UNIVERSALITY | MATHEMATICS, APPLIED | Benjamin-Ono equation | PHYSICS, MULTIDISCIPLINARY | INTERNAL WAVES | PHYSICS, MATHEMATICAL | MODULATION

Journal Article

Wave Motion, ISSN 0165-2125, 04/2020, Volume 94, p. 102502

Dispersive shock waves (DSWs) in the three dimensional Benjamin–Ono (3DBO) equation are studied with step-like initial condition along a paraboloid front...

Dispersive shock waves | Three dimensional Benjamin–Ono equation | Whitham modulation theory | FLUIDS | ACOUSTICS | MECHANICS | PHYSICS, MULTIDISCIPLINARY | INTERNAL WAVES | Three dimensional Benjamin-Ono equation | LIMIT | MODULATION

Dispersive shock waves | Three dimensional Benjamin–Ono equation | Whitham modulation theory | FLUIDS | ACOUSTICS | MECHANICS | PHYSICS, MULTIDISCIPLINARY | INTERNAL WAVES | Three dimensional Benjamin-Ono equation | LIMIT | MODULATION

Journal Article

SIAM journal on mathematical analysis, ISSN 1095-7154, 2019, Volume 51, Issue 4, pp. 3298 - 3323

We consider the fractional Korteweg-de Vries equation u(t) +uu(x) - vertical bar D vertical bar(alpha)u(x...

LIFE-SPAN | MATHEMATICS, APPLIED | WELL-POSEDNESS | dispersive equations | enhanced life span | WATER-WAVES | BENJAMIN-ONO-EQUATION | DISPERSIVE PERTURBATIONS | BURGERS | REGULARITY | fKdV | NORMAL FORMS | BLOW-UP | Mathematics - Analysis of PDEs

LIFE-SPAN | MATHEMATICS, APPLIED | WELL-POSEDNESS | dispersive equations | enhanced life span | WATER-WAVES | BENJAMIN-ONO-EQUATION | DISPERSIVE PERTURBATIONS | BURGERS | REGULARITY | fKdV | NORMAL FORMS | BLOW-UP | Mathematics - Analysis of PDEs

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2016, Volume 433, Issue 1, pp. 149 - 175

In this work we consider the initial value problem (IVP) associated to the two dimensional Zakharov–Kuznetsov...

Local well-posedness | Zakharov–Kuznetsov equation | Weighted Sobolev spaces | Zakharov-Kuznetsov equation | MATHEMATICS | MATHEMATICS, APPLIED | BENJAMIN-ONO-EQUATION | IVP | CAUCHY-PROBLEM | WELL-POSEDNESS

Local well-posedness | Zakharov–Kuznetsov equation | Weighted Sobolev spaces | Zakharov-Kuznetsov equation | MATHEMATICS | MATHEMATICS, APPLIED | BENJAMIN-ONO-EQUATION | IVP | CAUCHY-PROBLEM | WELL-POSEDNESS

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 12/2015, Volume 259, Issue 11, pp. 6694 - 6717

In this paper we analyze operator splitting for the Benjamin–Ono equation, ut=uux+Huxx, where H denotes the Hilbert transform...

Benjamin–Ono equation | Godunov splitting | Strang splitting | Error estimate | Convergence | Benjamin-Ono equation | MATHEMATICS | WAVES | GLOBAL WELL-POSEDNESS

Benjamin–Ono equation | Godunov splitting | Strang splitting | Error estimate | Convergence | Benjamin-Ono equation | MATHEMATICS | WAVES | GLOBAL WELL-POSEDNESS

Journal Article

Nonlinear Analysis, ISSN 0362-546X, 11/2019, Volume 188, pp. 50 - 69

In this work we prove that the initial value problem (IVP) associated to the two-dimensional Benjamin–Ono equation ut+HΔu+uux=0,(x,y)∈T2,t∈R,u(x,y,0)=u0(x,y...

Benjamin–Ono equation | Sobolev spaces | Well-posedness | MATHEMATICS | MATHEMATICS, APPLIED | Benjamin-Ono equation | GLOBAL WELL-POSEDNESS | Boundary value problems | Well posed problems | Sobolev space | Hilbert transformation | Cauchy problem

Benjamin–Ono equation | Sobolev spaces | Well-posedness | MATHEMATICS | MATHEMATICS, APPLIED | Benjamin-Ono equation | GLOBAL WELL-POSEDNESS | Boundary value problems | Well posed problems | Sobolev space | Hilbert transformation | Cauchy problem

Journal Article

Advances in Mathematics, ISSN 0001-8708, 04/2019, Volume 347, pp. 619 - 676

We consider the Cauchy problem for the defocusing cubic nonlinear Schrödinger equation in four space dimensions and establish almost sure local well-posedness...

Almost sure scattering | Nonlinear Schrödinger equation | Almost sure well-posedness | Random initial data | MATHEMATICS | BENJAMIN-ONO-EQUATION | INVARIANT-MEASURES | WAVE EQUATION | GLOBAL EXISTENCE | MAPS | REGULARITY | Nonlinear Schrodinger equation | DATA CAUCHY-THEORY

Almost sure scattering | Nonlinear Schrödinger equation | Almost sure well-posedness | Random initial data | MATHEMATICS | BENJAMIN-ONO-EQUATION | INVARIANT-MEASURES | WAVE EQUATION | GLOBAL EXISTENCE | MAPS | REGULARITY | Nonlinear Schrodinger equation | DATA CAUCHY-THEORY

Journal Article

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A numerical approach to blow-up issues for dispersive perturbations of Burgers' equation

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 03/2015, Volume 295-296, pp. 46 - 65

We provide a detailed numerical study of various issues pertaining to the dynamics of the Burgers' equation perturbed by a weak dispersive term...

Fractional Korteweg-de Vries equations | Whitham equations | Solitons | Blow-up | Fractional BBM equations | EXISTENCE | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | SMOOTHING PROPERTIES | TIME | DE-VRIES EQUATION | PHYSICS, MATHEMATICAL | BOUSSINESQ SYSTEM | WATER-WAVES | BENJAMIN-ONO-EQUATION | LONG WAVES | WHITHAM EQUATION | SOLITARY-WAVE SOLUTIONS

Fractional Korteweg-de Vries equations | Whitham equations | Solitons | Blow-up | Fractional BBM equations | EXISTENCE | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | SMOOTHING PROPERTIES | TIME | DE-VRIES EQUATION | PHYSICS, MATHEMATICAL | BOUSSINESQ SYSTEM | WATER-WAVES | BENJAMIN-ONO-EQUATION | LONG WAVES | WHITHAM EQUATION | SOLITARY-WAVE SOLUTIONS

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 12/2014, Volume 332, Issue 3, pp. 1203 - 1234

We consider the question of scattering for the boson star equation in three space dimensions...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | SPACE | BENJAMIN-ONO-EQUATION | LARGE TIME | COLLAPSE | SEMIRELATIVISTIC HARTREE-EQUATIONS | NONLINEAR SCHRODINGER | ASYMPTOTICS | INITIAL DATA | PHYSICS, MATHEMATICAL | GLOBAL-SOLUTIONS

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | SPACE | BENJAMIN-ONO-EQUATION | LARGE TIME | COLLAPSE | SEMIRELATIVISTIC HARTREE-EQUATIONS | NONLINEAR SCHRODINGER | ASYMPTOTICS | INITIAL DATA | PHYSICS, MATHEMATICAL | GLOBAL-SOLUTIONS

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 10/2016, Volume 333, pp. 84 - 98

Dispersive shock waves (DSWs) in the Kadomtsev–Petviashvili (KP) equation and two dimensional Benjamin–Ono (2DBO...

Dispersive shock waves | Kadomtsev–Petviashvili equation | Two dimensional Benjamin–Ono equation | FLUIDS | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | GREAT DEPTH | Kadomtsev-Petviashvili equation | LIMIT | PHYSICS, MATHEMATICAL | KORTEWEG-DEVRIES EQUATION | WATER-WAVES | EVOLUTION | SOLITARY WAVES | INTERNAL WAVES | Two dimensional Benjamin-Ono equation | TRANSFORM | Numerical analysis

Dispersive shock waves | Kadomtsev–Petviashvili equation | Two dimensional Benjamin–Ono equation | FLUIDS | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | GREAT DEPTH | Kadomtsev-Petviashvili equation | LIMIT | PHYSICS, MATHEMATICAL | KORTEWEG-DEVRIES EQUATION | WATER-WAVES | EVOLUTION | SOLITARY WAVES | INTERNAL WAVES | Two dimensional Benjamin-Ono equation | TRANSFORM | Numerical analysis

Journal Article

Stratum Plus, ISSN 1608-9057, 2018, Volume 34, Issue 5, pp. 1563 - 1608

We prove that the modified Korteweg-de Vries (mKdV) equation is unconditionally well-posed in H-s (R) for s > 1/3...

Modified energy | Unconditional uniqueness | Modified Korteweg-de Vries equation | Well-posedness | MATHEMATICS | well-posedness | CAUCHY-PROBLEM | LOW REGULARITY | modified energy | LOCAL WELL-POSEDNESS | MODIFIED KDV EQUATION | BENJAMIN-ONO | ILL-POSEDNESS | unconditional uniqueness

Modified energy | Unconditional uniqueness | Modified Korteweg-de Vries equation | Well-posedness | MATHEMATICS | well-posedness | CAUCHY-PROBLEM | LOW REGULARITY | modified energy | LOCAL WELL-POSEDNESS | MODIFIED KDV EQUATION | BENJAMIN-ONO | ILL-POSEDNESS | unconditional uniqueness

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 07/2012, Volume 263, Issue 1, pp. 1 - 24

We consider Schrödinger equations in R1+2 with electro-magnetic potentials. The potentials belong to H1, and typically they are time-independent or determined as solutions to inhomogeneous wave equations...

Maxwell–Schrödinger equations | Smoothing effect | Well-posedness | Maxwell-Schrödinger equations | MAGNETIC POTENTIALS | EXISTENCE | STRICHARTZ | CAUCHY-PROBLEM | LOCAL WELL-POSEDNESS | BENJAMIN-ONO EQUATIONS | MATHEMATICS | NONLINEAR KLEIN-GORDON | Maxwell-Schrodinger equations | DISPERSIVE EQUATIONS | FINITE-ENERGY SOLUTIONS | OPERATORS

Maxwell–Schrödinger equations | Smoothing effect | Well-posedness | Maxwell-Schrödinger equations | MAGNETIC POTENTIALS | EXISTENCE | STRICHARTZ | CAUCHY-PROBLEM | LOCAL WELL-POSEDNESS | BENJAMIN-ONO EQUATIONS | MATHEMATICS | NONLINEAR KLEIN-GORDON | Maxwell-Schrodinger equations | DISPERSIVE EQUATIONS | FINITE-ENERGY SOLUTIONS | OPERATORS

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2018, Volume 460, Issue 2, pp. 1004 - 1018

In this work we consider the initial value problem (IVP) associated to the Ostrovsky equationsut+∂x3u±∂x−1u+u∂xu=0,x∈R,t∈R,u(x,0)=u0(x).} We study the...

Ostrovsky equation | Local well-posedness | Weighted Sobolev spaces | MATHEMATICS | MATHEMATICS, APPLIED | BENJAMIN-ONO-EQUATION | REGULARITY | CAUCHY-PROBLEM | WELL-POSEDNESS | KDV EQUATION

Ostrovsky equation | Local well-posedness | Weighted Sobolev spaces | MATHEMATICS | MATHEMATICS, APPLIED | BENJAMIN-ONO-EQUATION | REGULARITY | CAUCHY-PROBLEM | WELL-POSEDNESS | KDV EQUATION

Journal Article

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SCATTERING FOR DEFOCUSING GENERALIZED BENJAMIN-ONO EQUATION IN THE ENERGY SPACE H-1/2 (R)

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, ISSN 0002-9947, 10/2019, Volume 372, Issue 7, pp. 5011 - 5067

We prove the scattering for the defocusing generalized Benjamin-Ono equation in the energy space H-1/2 (R...

MATHEMATICS | Generalized Benjamin-Ono equation | scattering | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | FINITE-TIME BLOWUP | monotonicity | NONLINEAR SCHRODINGER-EQUATION | GLOBAL WELL-POSEDNESS

MATHEMATICS | Generalized Benjamin-Ono equation | scattering | CALCULUS | CONCENTRATION-COMPACTNESS PRINCIPLE | FINITE-TIME BLOWUP | monotonicity | NONLINEAR SCHRODINGER-EQUATION | GLOBAL WELL-POSEDNESS

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 02/2016, Volume 270, Issue 3, pp. 976 - 1000

We shall deduce some special regularity properties of solutions to the IVP associated to the Benjamin–Ono equation...

Benjamin–Ono equation | Weighted Sobolev spaces | Benjamin-Ono equation | MATHEMATICS | CAUCHY-PROBLEM | GLOBAL WELL-POSEDNESS

Benjamin–Ono equation | Weighted Sobolev spaces | Benjamin-Ono equation | MATHEMATICS | CAUCHY-PROBLEM | GLOBAL WELL-POSEDNESS

Journal Article

Studies in Applied Mathematics, ISSN 0022-2526, 02/2018, Volume 140, Issue 2, pp. 133 - 177

The aim of this paper is to study, via theoretical analysis and numerical simulations, the dynamics of Whitham and related equations...

EXISTENCE | MATHEMATICS, APPLIED | DISPERSIVE PERTURBATIONS | STABILITY | SOLITARY-WAVE SOLUTIONS | KORTEWEG-DE-VRIES | BLOW-UP | BENJAMIN-ONO | MODEL | SURFACE-WATER WAVES | POSEDNESS | Analysis of PDEs | Mathematics

EXISTENCE | MATHEMATICS, APPLIED | DISPERSIVE PERTURBATIONS | STABILITY | SOLITARY-WAVE SOLUTIONS | KORTEWEG-DE-VRIES | BLOW-UP | BENJAMIN-ONO | MODEL | SURFACE-WATER WAVES | POSEDNESS | Analysis of PDEs | Mathematics

Journal Article

Mathematical methods in the applied sciences, ISSN 1099-1476, 2018, Volume 42, Issue 1, pp. 219 - 228

In this paper, we study several aspects of solitary wave solutions of the rotation Benjamin‐Ono equation...

Benjamin‐Ono | solitary waves | Benjamin-Ono | MATHEMATICS, APPLIED | STANDING WAVES | INTERNAL WAVES | Orbital stability | Ground state | Traveling waves | Solitary waves | Rotation

Benjamin‐Ono | solitary waves | Benjamin-Ono | MATHEMATICS, APPLIED | STANDING WAVES | INTERNAL WAVES | Orbital stability | Ground state | Traveling waves | Solitary waves | Rotation

Journal Article

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