1.
Classical methods in ordinary differential equations

: with applications to boundary value problems

2012, Graduate studies in mathematics, ISBN 0821846949, Volume 129, xvii, 373

Book

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2017, Volume 453, Issue 1, pp. 271 - 286

Recently, Leray's problem of the -decay of a special weak solution to the Navier–Stokes equations with nonhomogeneous boundary values was studied by the...

Instationary Navier–Stokes equations | Weak solutions | Time-dependent data | Exterior domain | Asymptotic behavior | Nonzero boundary values | SYSTEM | MATHEMATICS, APPLIED | SPACES | NONHOMOGENEOUS DATA | EQUATIONS | MATHEMATICS | EXTERIOR DOMAINS | Instationary Navier-Stokes equations | REGULARITY CONDITIONS | Fluid dynamics

Instationary Navier–Stokes equations | Weak solutions | Time-dependent data | Exterior domain | Asymptotic behavior | Nonzero boundary values | SYSTEM | MATHEMATICS, APPLIED | SPACES | NONHOMOGENEOUS DATA | EQUATIONS | MATHEMATICS | EXTERIOR DOMAINS | Instationary Navier-Stokes equations | REGULARITY CONDITIONS | Fluid dynamics

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 11/2016, Volume 72, Issue 9, pp. 2486 - 2504

In this paper, a -dimensional generalized B-type Kadomtsev–Petviashvili equation is investigated, which can be used to describe weakly dispersive waves...

Riemann theta function | Soliton solution | A [formula omitted]-dimensional generalized B-type Kadomtsev–Petviashvili equation | Periodic solution | Bell polynomials | A (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation | DIMENSIONS | MATHEMATICS, APPLIED | SYMMETRIES | Kadomtsev-Petviashvili equation | NONLINEAR EVOLUTION-EQUATIONS | DARBOUX TRANSFORMATIONS | A (3+1)-dimensional generalized B-type | RATIONAL CHARACTERISTICS | Fluid dynamics | Wave propagation | Amplitudes | Computational fluid dynamics | Asymptotic properties | Mathematical analysis | Mathematical models | Polynomials | Combinatorial analysis

Riemann theta function | Soliton solution | A [formula omitted]-dimensional generalized B-type Kadomtsev–Petviashvili equation | Periodic solution | Bell polynomials | A (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation | DIMENSIONS | MATHEMATICS, APPLIED | SYMMETRIES | Kadomtsev-Petviashvili equation | NONLINEAR EVOLUTION-EQUATIONS | DARBOUX TRANSFORMATIONS | A (3+1)-dimensional generalized B-type | RATIONAL CHARACTERISTICS | Fluid dynamics | Wave propagation | Amplitudes | Computational fluid dynamics | Asymptotic properties | Mathematical analysis | Mathematical models | Polynomials | Combinatorial analysis

Journal Article

1978, International series in pure and applied mathematics, ISBN 007004452X, xiv, 593

Book

5.
Full Text
Global solutions and self‐similar solutions for coupled nonlinear Schrödinger equations

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 08/2017, Volume 40, Issue 12, pp. 4613 - 4624

In this paper, we prove the existence and uniqueness for the global solutions of Cauchy problem for coupled nonlinear Schrödinger equations and obtain the...

global solutions | self‐similar solutions | 35Q55 | subclass 35A05 | coupled nonlinear Schrödinger equations | 37K10 | Cauchy problem | self-similar solutions | MATHEMATICS, APPLIED | SOLITONS | coupled nonlinear Schrodinger equations | CAUCHY-PROBLEM | PROGRESSING WAVES | BLOW-UP | Asymptotic properties | Mathematical analysis | Decay | Uniqueness | Self-similarity

global solutions | self‐similar solutions | 35Q55 | subclass 35A05 | coupled nonlinear Schrödinger equations | 37K10 | Cauchy problem | self-similar solutions | MATHEMATICS, APPLIED | SOLITONS | coupled nonlinear Schrodinger equations | CAUCHY-PROBLEM | PROGRESSING WAVES | BLOW-UP | Asymptotic properties | Mathematical analysis | Decay | Uniqueness | Self-similarity

Journal Article

Applied Mathematics Letters, ISSN 0893-9659, 09/2017, Volume 71, pp. 44 - 50

Let be a nonnegative radical potential in a cylinder. In this paper, we study the solutions of the Dirichlet–Sch problem associated with a stationary...

Dirichlet–Sch problem | Asymptotic property | Schrödinger equation | MATHEMATICS, APPLIED | Schrodinger equation | Dirichlet-Sch problem | CYLINDER | CONE | Information science

Dirichlet–Sch problem | Asymptotic property | Schrödinger equation | MATHEMATICS, APPLIED | Schrodinger equation | Dirichlet-Sch problem | CYLINDER | CONE | Information science

Journal Article

1996, Translations of mathematical monographs, ISBN 0821805363, Volume 151., xvi, 176

Book

1978, ISBN 9780444851727, Volume 5., xxiv, 700

Book

Physical Review D - Particles, Fields, Gravitation and Cosmology, ISSN 1550-7998, 12/2015, Volume 92, Issue 12

Extensions of Einstein gravity with quadratic curvature terms in the action arise in most effective theories of quantized gravity, including string theory....

FREE QUANTUM-THEORY | ENERGY | ASTRONOMY & ASTROPHYSICS | BLACK-HOLES | PHYSICS, PARTICLES & FIELDS | Gravitation | Asymptotic properties | Mathematical analysis | Flats | Cosmology | Horizon | Coupling | Symmetry

FREE QUANTUM-THEORY | ENERGY | ASTRONOMY & ASTROPHYSICS | BLACK-HOLES | PHYSICS, PARTICLES & FIELDS | Gravitation | Asymptotic properties | Mathematical analysis | Flats | Cosmology | Horizon | Coupling | Symmetry

Journal Article

Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 06/2018, Volume 41, pp. 334 - 361

The long-time asymptotics and bright -soliton solutions of the Kundu–Eckhaus equation are studied by Riemann–Hilbert approach. Firstly, the initial value...

Long-time asymptotics | Soliton solutions | Lax pair | Kundu–Eckhaus equation | Riemann–Hilbert approach | MATHEMATICS, APPLIED | WAVES | Riemann-Hilbert approach | LIMIT | Kundu-Eckhaus equation | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | Information science

Long-time asymptotics | Soliton solutions | Lax pair | Kundu–Eckhaus equation | Riemann–Hilbert approach | MATHEMATICS, APPLIED | WAVES | Riemann-Hilbert approach | LIMIT | Kundu-Eckhaus equation | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | Information science

Journal Article

1997, Lecture notes in mathematics, ISBN 3540634347, Volume 1668, xiv, 203

Book

Journal of Differential Equations, ISSN 0022-0396, 05/2017, Volume 262, Issue 10, pp. 4907 - 4930

In this paper we study a free boundary problem modeling the growth of solid tumor spheroid. It consists of two elliptic equations describing nutrient diffusion...

Asymptotic stability | Free boundary problem | Tumor spheroid | Gibbs–Thomson relation | Well-posedness | MATHEMATICS | INSTABILITY | SYMMETRY-BREAKING BIFURCATIONS | STABILITY | STATIONARY SOLUTIONS | GROWTH | Gibbs Thomson relation | INHIBITORS | Models | Tumors

Asymptotic stability | Free boundary problem | Tumor spheroid | Gibbs–Thomson relation | Well-posedness | MATHEMATICS | INSTABILITY | SYMMETRY-BREAKING BIFURCATIONS | STABILITY | STATIONARY SOLUTIONS | GROWTH | Gibbs Thomson relation | INHIBITORS | Models | Tumors

Journal Article

1992, Lezioni lincee., ISBN 9780521420235, 155

The theme of this book is the investigation of globally asymptotic solutions of evolutionary equations. Locally asymptotic solutions of the Navier–Stokes...

Evolution equations | Asymptotic theory

Evolution equations | Asymptotic theory

Book

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 11/2012, Volume 45, Issue 47, pp. 475202 - 31

In a previous study (Matsuno Y 2012 J. Phys. A: Math. Theor. 45 23202), we have developed a systematic method for obtaining the bright soliton solutions of the...

PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Dependent variables | Asymptotic properties | Mathematical analysis | Solitons | Plane waves | Nonlinearity | Boundary conditions | Schroedinger equation | Derivatives

PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Dependent variables | Asymptotic properties | Mathematical analysis | Solitons | Plane waves | Nonlinearity | Boundary conditions | Schroedinger equation | Derivatives

Journal Article

1976, Lecture notes in mathematics, ISBN 0387076980, Volume 522., 104

Book

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 06/2017, Volume 450, Issue 1, pp. 152 - 168

This paper concerns the study of the asymptotic behavior of solutions to reaction–diffusion systems modeling multi-components reversible chemistry with spatial...

Reaction–diffusion equation | Chemical reaction | Entropy method | Asymptotic behavior | Renormalized solution | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | EQUATIONS | MATHEMATICS | ENTROPY METHODS | L-1 | Reaction-diffusion equation | EXPONENTIAL DECAY | EQUILIBRIUM | MASS | Trucks | Four-wheel drive | or physical chemistry | Mathematics | Analysis of PDEs | Chemical Sciences | Theoretical and

Reaction–diffusion equation | Chemical reaction | Entropy method | Asymptotic behavior | Renormalized solution | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | EQUATIONS | MATHEMATICS | ENTROPY METHODS | L-1 | Reaction-diffusion equation | EXPONENTIAL DECAY | EQUILIBRIUM | MASS | Trucks | Four-wheel drive | or physical chemistry | Mathematics | Analysis of PDEs | Chemical Sciences | Theoretical and

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 1/2017, Volume 87, Issue 2, pp. 1069 - 1080

In this paper, we consider the (3 $$+$$ + 1)-dimensional water wave equation $$u_{yzt}+u_{xxxyz}-6u_{x}u_{xyz}-6u_{xy}u_{xz}=0.$$ u y z t + u x x x y z - 6 u x...

Engineering | Vibration, Dynamical Systems, Control | Asymptotic property | Bell polynomials | Classical Mechanics | Hirota bilinear equation | Automotive Engineering | Mechanical Engineering | (3+1)-Dimensional equation | Riemann theta solution | DARBOUX TRANSFORMATION | ION-ACOUSTIC SOLITONS | DE-VRIES EQUATION | MULTIPLE-SOLITON-SOLUTIONS | ENGINEERING, MECHANICAL | BACKLUND TRANSFORMATION | SHALLOW-WATER | MULTISOLITON SOLUTIONS | MECHANICS | MAXWELL-BLOCH SYSTEM | SINGULAR SOLITONS | SPATIOTEMPORAL DISPERSION | Water waves | Asymptotic properties | Mathematical analysis | Wave equations | Polynomials | Solitary waves | Combinatorial analysis

Engineering | Vibration, Dynamical Systems, Control | Asymptotic property | Bell polynomials | Classical Mechanics | Hirota bilinear equation | Automotive Engineering | Mechanical Engineering | (3+1)-Dimensional equation | Riemann theta solution | DARBOUX TRANSFORMATION | ION-ACOUSTIC SOLITONS | DE-VRIES EQUATION | MULTIPLE-SOLITON-SOLUTIONS | ENGINEERING, MECHANICAL | BACKLUND TRANSFORMATION | SHALLOW-WATER | MULTISOLITON SOLUTIONS | MECHANICS | MAXWELL-BLOCH SYSTEM | SINGULAR SOLITONS | SPATIOTEMPORAL DISPERSION | Water waves | Asymptotic properties | Mathematical analysis | Wave equations | Polynomials | Solitary waves | Combinatorial analysis

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 10/2015, Volume 82, Issue 1-2, pp. 333 - 347

In this paper, a -dimensional generalized shallow water wave equation is investigated through bilinear Hirota method. Interestingly, the breather-type and...

Riemann theta function | Hirota bilinear method | (2 + 1)-dimensional GSWW equation | Lump-type soliton | Breather-type soliton | Quasi-periodic wave solution | Asymptotic analysis | EXCITATIONS | DIFFERENTIAL-EQUATIONS | KADOMTSEV-PETVIASHVILI EQUATION | ENGINEERING, MECHANICAL | MECHANICS | LINEAR EVOLUTION-EQUATIONS | NONLINEAR EQUATIONS | (2+1)-dimensional GSWW equation | SYMBOLIC COMPUTATION | BILINEAR EQUATIONS | KDV EQUATION | TRANSFORM | RATIONAL CHARACTERISTICS | Water waves | Asymptotic properties | Asymptotic methods | Shallow water | Solitary waves | Wave equations

Riemann theta function | Hirota bilinear method | (2 + 1)-dimensional GSWW equation | Lump-type soliton | Breather-type soliton | Quasi-periodic wave solution | Asymptotic analysis | EXCITATIONS | DIFFERENTIAL-EQUATIONS | KADOMTSEV-PETVIASHVILI EQUATION | ENGINEERING, MECHANICAL | MECHANICS | LINEAR EVOLUTION-EQUATIONS | NONLINEAR EQUATIONS | (2+1)-dimensional GSWW equation | SYMBOLIC COMPUTATION | BILINEAR EQUATIONS | KDV EQUATION | TRANSFORM | RATIONAL CHARACTERISTICS | Water waves | Asymptotic properties | Asymptotic methods | Shallow water | Solitary waves | Wave equations

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 12/2015, Volume 82, Issue 4, pp. 2031 - 2049

Under investigation in this paper is a generalized -dimensional Korteweg-de Vries equation, which could describe many nonlinear phenomena in plasma physics. By...

Bell’s polynomials | Soliton solution | A generalized (2+1)-dimensional KdV equation | Periodic wave solution | Bilinear Bäcklund transformation | Lax pairs | TRANSFORMATION | MODEL | KADOMTSEV-PETVIASHVILI EQUATION | ENGINEERING, MECHANICAL | FIBERS | MECHANICS | SOLITONS | Bilinear Backlund transformation | BILINEAR EQUATIONS | NONLINEAR EVOLUTION-EQUATIONS | RATIONAL CHARACTERISTICS | TODA LATTICE | Bell's polynomials | HIERARCHY | Plasma physics | Conservation laws | Nonlinear phenomena | Asymptotic properties | Polynomials | Plasma (physics) | Solitary waves

Bell’s polynomials | Soliton solution | A generalized (2+1)-dimensional KdV equation | Periodic wave solution | Bilinear Bäcklund transformation | Lax pairs | TRANSFORMATION | MODEL | KADOMTSEV-PETVIASHVILI EQUATION | ENGINEERING, MECHANICAL | FIBERS | MECHANICS | SOLITONS | Bilinear Backlund transformation | BILINEAR EQUATIONS | NONLINEAR EVOLUTION-EQUATIONS | RATIONAL CHARACTERISTICS | TODA LATTICE | Bell's polynomials | HIERARCHY | Plasma physics | Conservation laws | Nonlinear phenomena | Asymptotic properties | Polynomials | Plasma (physics) | Solitary waves

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 05/2017, Volume 347, pp. 1 - 11

The Fourier-transformed version of the time dependent slip-flow model Boltzmann equation associated with the linearized BGK model is solved in order to...

Linearized Boltzmann equation | Rarefied slip flow equation | Asymptotics of elementary solutions | Grossly determined solutions | MATHEMATICS, APPLIED | GAS-DYNAMICS | KINETIC-THEORY | PHYSICS, MULTIDISCIPLINARY | TRANSPORT-EQUATION | PHYSICS, MATHEMATICAL

Linearized Boltzmann equation | Rarefied slip flow equation | Asymptotics of elementary solutions | Grossly determined solutions | MATHEMATICS, APPLIED | GAS-DYNAMICS | KINETIC-THEORY | PHYSICS, MULTIDISCIPLINARY | TRANSPORT-EQUATION | PHYSICS, MATHEMATICAL

Journal Article

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