Optik - International Journal for Light and Electron Optics, ISSN 0030-4026, 06/2016, Volume 127, Issue 12, pp. 4970 - 4983

This paper studies the exact solutions with parameters and optical soliton solutions of the (2+1)-dimensional hyperbolic nonlinear Schrödinger equation which...

Bright–dark-singular soliton solutions | Hyperbolic nonlinear Schrödinger equation | The soliton ansatz method | Modified simple equation method | Exp-function method | Bright-dark-singular soliton solutions | TRAVELING-WAVE SOLUTIONS | EVOLUTION | Hyperbolic nonlinear Schrodinger equation | OPTICS | TANH-FUNCTION METHOD | MEW | Mathematical analysis | Exact solutions | Solitons | Nonlinearity | Evolution | Schroedinger equation | Trigonometric functions | Solitary waves

Bright–dark-singular soliton solutions | Hyperbolic nonlinear Schrödinger equation | The soliton ansatz method | Modified simple equation method | Exp-function method | Bright-dark-singular soliton solutions | TRAVELING-WAVE SOLUTIONS | EVOLUTION | Hyperbolic nonlinear Schrodinger equation | OPTICS | TANH-FUNCTION METHOD | MEW | Mathematical analysis | Exact solutions | Solitons | Nonlinearity | Evolution | Schroedinger equation | Trigonometric functions | Solitary waves

Journal Article

Physics Letters A, ISSN 0375-9601, 2009, Volume 373, Issue 21, pp. 1844 - 1846

In this work, four ( 2 + 1 ) -dimensional nonlinear evolution equations, generated by the Jaulent–Miodek hierarchy, are investigated. The necessary condition...

Multiple kink solutions | Multiple singular kink solutions | Nonlinear [formula omitted]-dimensional equation | Hirota bilinear method | Nonlinear (2 + 1)-dimensional equation | HIROTA 3-SOLITON CONDITION | PHYSICS, MULTIDISCIPLINARY | BURGERS EQUATIONS | FRONT SOLUTIONS | SEARCH | Nonlinear (2+1)-dimensional equation | SHALLOW-WATER WAVES | EVOLUTION-EQUATIONS | TANH-COTH METHOD | KP EQUATION | BILINEAR EQUATIONS | N-SOLITON SOLUTION

Multiple kink solutions | Multiple singular kink solutions | Nonlinear [formula omitted]-dimensional equation | Hirota bilinear method | Nonlinear (2 + 1)-dimensional equation | HIROTA 3-SOLITON CONDITION | PHYSICS, MULTIDISCIPLINARY | BURGERS EQUATIONS | FRONT SOLUTIONS | SEARCH | Nonlinear (2+1)-dimensional equation | SHALLOW-WATER WAVES | EVOLUTION-EQUATIONS | TANH-COTH METHOD | KP EQUATION | BILINEAR EQUATIONS | N-SOLITON SOLUTION

Journal Article

International Journal of Heat and Mass Transfer, ISSN 0017-9310, 11/2017, Volume 114, pp. 1126 - 1134

•The time-dependent fundamental solution of the convection-diffusion problem is derived.•The singular boundary method is first applied to the transient...

Convection-diffusion | Origin intensity factors | Time-dependent fundamental solution | Singular boundary method | MECHANICS | DUAL RECIPROCITY | THERMODYNAMICS | PHASE-CHANGE PROBLEMS | ELEMENT METHOD | EQUATIONS | FORMULATION | ENGINEERING, MECHANICAL | Hydrology | Aquatic resources | Numerical analysis | Synthetic training devices | Methods

Convection-diffusion | Origin intensity factors | Time-dependent fundamental solution | Singular boundary method | MECHANICS | DUAL RECIPROCITY | THERMODYNAMICS | PHASE-CHANGE PROBLEMS | ELEMENT METHOD | EQUATIONS | FORMULATION | ENGINEERING, MECHANICAL | Hydrology | Aquatic resources | Numerical analysis | Synthetic training devices | Methods

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 7/2016, Volume 85, Issue 2, pp. 813 - 816

This paper applied the trial solution technique to chiral nonlinear Schrodinger’s equation in (1 $$+$$ + 2)-dimensions. This led to solitons and other...

Chiral NLSE | Engineering | Vibration, Dynamical Systems, Control | Solitons and singular periodic solutions | Mechanics | Trial solution technique | Automotive Engineering | Mechanical Engineering | Solitary waves | Nonlinear equations | Schroedinger equation

Chiral NLSE | Engineering | Vibration, Dynamical Systems, Control | Solitons and singular periodic solutions | Mechanics | Trial solution technique | Automotive Engineering | Mechanical Engineering | Solitary waves | Nonlinear equations | Schroedinger equation

Journal Article

Physics Letters A, ISSN 0375-9601, 2009, Volume 373, Issue 33, pp. 2927 - 2930

Two ( 2 + 1 ) -dimensional shallow water wave equations are studied. The Hirota bilinear method is used to determine the multiple soliton solutions for these...

Multiple singular soliton solutions | Multiple soliton solutions | Hirota bilinear method | PHYSICS, MULTIDISCIPLINARY | BURGERS EQUATIONS

Multiple singular soliton solutions | Multiple soliton solutions | Hirota bilinear method | PHYSICS, MULTIDISCIPLINARY | BURGERS EQUATIONS

Journal Article

NONLINEAR DYNAMICS, ISSN 0924-090X, 07/2016, Volume 85, Issue 2, pp. 813 - 816

This paper applied the trial solution technique to chiral nonlinear Schrodinger's equation in (12)-dimensions. This led to solitons and other solutions to the...

Chiral NLSE | MECHANICS | ALFVEN WAVES | SOLITONS | APPROXIMATION | Solitons and singular periodic solutions | PERTURBATION | Trial solution technique | ENGINEERING, MECHANICAL

Chiral NLSE | MECHANICS | ALFVEN WAVES | SOLITONS | APPROXIMATION | Solitons and singular periodic solutions | PERTURBATION | Trial solution technique | ENGINEERING, MECHANICAL

Journal Article

Boundary Value Problems, ISSN 1687-2762, 12/2017, Volume 2017, Issue 1, pp. 1 - 30

A ( 3 + 1 ) $(3+1)$ -dimensional boundary value problem for equations of Keldysh type (the second kind) is studied. Such problems for equations of Tricomi...

Mathematics | 35M12 | generalized solutions | Ordinary Differential Equations | uniqueness | Analysis | weakly hyperbolic equations | boundary value problems | Difference and Functional Equations | Approximations and Expansions | 35D30 | Mathematics, general | 35A20 | behavior of solution | Partial Differential Equations | SINGULAR SOLUTIONS | MATHEMATICS | MATHEMATICS, APPLIED | DARBOUX PROBLEM | LINE | BOUNDARY-VALUE-PROBLEMS | NONTRIVIAL SOLUTIONS | Boundary value problems | Planes | Singularities | Analogue | Mathematical analysis | Uniqueness | Texts | Estimates

Mathematics | 35M12 | generalized solutions | Ordinary Differential Equations | uniqueness | Analysis | weakly hyperbolic equations | boundary value problems | Difference and Functional Equations | Approximations and Expansions | 35D30 | Mathematics, general | 35A20 | behavior of solution | Partial Differential Equations | SINGULAR SOLUTIONS | MATHEMATICS | MATHEMATICS, APPLIED | DARBOUX PROBLEM | LINE | BOUNDARY-VALUE-PROBLEMS | NONTRIVIAL SOLUTIONS | Boundary value problems | Planes | Singularities | Analogue | Mathematical analysis | Uniqueness | Texts | Estimates

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 10/2016, Volume 289, pp. 311 - 323

This study adopts the corrected Fourier series expansion method with only limited smooth degree to solve the Legendre equation with an arbitrary complex...

Classical solution | Unified solution | Corrected Fourier series | Generalized solution | Singular function | MATHEMATICS, APPLIED | Differential equations

Classical solution | Unified solution | Corrected Fourier series | Generalized solution | Singular function | MATHEMATICS, APPLIED | Differential equations

Journal Article

Computer Methods in Applied Mechanics and Engineering, ISSN 0045-7825, 06/2015, Volume 290, pp. 127 - 155

A new strategy for the efficient solution of highly nonlinear structural problems is proposed, based on the combined use of Domain Decomposition (DD) and...

Elasto-plasticity | Singular Value Decomposition (SVD) | Domain Decomposition (DD) | Proper Orthogonal Decomposition (POD) | Non-linear Model Order Reduction (MOR) | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | MECHANICAL SYSTEMS | SIMULATION | PROPER ORTHOGONAL DECOMPOSITION | Usage | Models | Green technology | Nonlinear dynamics | Order reduction | Computer simulation | Strategy | Nonlinearity | Mathematical models | Domain decomposition | Adaptation

Elasto-plasticity | Singular Value Decomposition (SVD) | Domain Decomposition (DD) | Proper Orthogonal Decomposition (POD) | Non-linear Model Order Reduction (MOR) | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | ENGINEERING, MULTIDISCIPLINARY | MECHANICAL SYSTEMS | SIMULATION | PROPER ORTHOGONAL DECOMPOSITION | Usage | Models | Green technology | Nonlinear dynamics | Order reduction | Computer simulation | Strategy | Nonlinearity | Mathematical models | Domain decomposition | Adaptation

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2008, Volume 204, Issue 2, pp. 817 - 823

In this work we study the (2 + 1)-dimensional Painlevé integrable Burgers equation. Multiple kink solutions and multiple singular kink solutions are formally...

(2 + 1)-Dimensional Burgers equations | Kink solutions | Singular kink solutions | Hirota bilinear method | MATHEMATICS, APPLIED | HIROTA 3-SOLITON CONDITION | (2+1)-Dimensional Burgers equations | SHALLOW-WATER WAVES | RATIONAL EXPANSION METHOD | SOLITON SOLUTIONS | COMPLEXITON SOLUTIONS | TANH-COTH METHOD | SYMBOLIC COMPUTATION | BILINEAR EQUATIONS | NONLINEAR EVOLUTION-EQUATIONS | MODEL-EQUATIONS

(2 + 1)-Dimensional Burgers equations | Kink solutions | Singular kink solutions | Hirota bilinear method | MATHEMATICS, APPLIED | HIROTA 3-SOLITON CONDITION | (2+1)-Dimensional Burgers equations | SHALLOW-WATER WAVES | RATIONAL EXPANSION METHOD | SOLITON SOLUTIONS | COMPLEXITON SOLUTIONS | TANH-COTH METHOD | SYMBOLIC COMPUTATION | BILINEAR EQUATIONS | NONLINEAR EVOLUTION-EQUATIONS | MODEL-EQUATIONS

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 06/2018, Volume 41, Issue 9, pp. 3430 - 3440

This paper deals with 2 core aspects of fractional calculus including existence of positive solution and Hyers‐Ulam stability for a class of singular...

Hyers‐Ulam stability | Caputo's fractional derivative | existence of positive solution | singular fractional differential equations | Hyers-Ulam stability | EXISTENCE | MATHEMATICS, APPLIED | SYSTEMS | Differential equations | Operators (mathematics) | Nonlinear equations | Green's functions | Mathematical analysis | Integral equations | Existence theorems | Stability analysis | Banach space | Fractional calculus

Hyers‐Ulam stability | Caputo's fractional derivative | existence of positive solution | singular fractional differential equations | Hyers-Ulam stability | EXISTENCE | MATHEMATICS, APPLIED | SYSTEMS | Differential equations | Operators (mathematics) | Nonlinear equations | Green's functions | Mathematical analysis | Integral equations | Existence theorems | Stability analysis | Banach space | Fractional calculus

Journal Article

IEEE Transactions on Antennas and Propagation, ISSN 0018-926X, 08/2008, Volume 56, Issue 8, pp. 2314 - 2324

The multilevel matrix decomposition algorithm (MLMDA) was originally developed by Michielsen and Boag for 2D TMz scattering problems and later implemented in...

multilayer Green's function | Transmission line matrix methods | Scattering | method of moments (MoM) | Matrix decomposition | Fast integral equation methods | printed antennas | Integral equations | Approximation algorithms | Iterative algorithms | MLFMA | Iterative methods | Moment methods | Singular value decomposition | Method of moments (MoM) | Multilayer Green's function | Printed antennas | FAST MULTIPOLE ALGORITHM | APPROXIMATION | fast integral equation methods | 3-D | ELECTROMAGNETIC SCATTERING | TELECOMMUNICATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | Evaluation | Algorithms | Potential theory (Mathematics) | Research | Methods | Decomposition (Mathematics) | Studies | Errors | Compressing | Computation | Mathematical analysis | Decomposition | Three dimensional

multilayer Green's function | Transmission line matrix methods | Scattering | method of moments (MoM) | Matrix decomposition | Fast integral equation methods | printed antennas | Integral equations | Approximation algorithms | Iterative algorithms | MLFMA | Iterative methods | Moment methods | Singular value decomposition | Method of moments (MoM) | Multilayer Green's function | Printed antennas | FAST MULTIPOLE ALGORITHM | APPROXIMATION | fast integral equation methods | 3-D | ELECTROMAGNETIC SCATTERING | TELECOMMUNICATIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | Evaluation | Algorithms | Potential theory (Mathematics) | Research | Methods | Decomposition (Mathematics) | Studies | Errors | Compressing | Computation | Mathematical analysis | Decomposition | Three dimensional

Journal Article

Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 8/2017, Volume 24, Issue 4, pp. 1 - 33

The chemotaxis system $$\begin{aligned} \left\{ \begin{array}{l} u_t = \Delta u - \chi \nabla \cdot \left( \frac{u}{v}\nabla v\right) , \\ v_t=\Delta v - v+u,...

Logarithmic sensitivity | 35D99 | Generalized solution | Analysis | Global existence | Mathematics | 92C17 | Chemotaxis | 35K55 | EXISTENCE | MATHEMATICS, APPLIED | SINGULAR SENSITIVITY | MODELS | PARABOLIC CHEMOTAXIS SYSTEM | BOUNDEDNESS

Logarithmic sensitivity | 35D99 | Generalized solution | Analysis | Global existence | Mathematics | 92C17 | Chemotaxis | 35K55 | EXISTENCE | MATHEMATICS, APPLIED | SINGULAR SENSITIVITY | MODELS | PARABOLIC CHEMOTAXIS SYSTEM | BOUNDEDNESS

Journal Article

Boundary Value Problems, ISSN 1687-2762, 12/2015, Volume 2015, Issue 1, pp. 1 - 11

Based on a variational approach, we prove that a second-order singular damped differential equation has at least one periodic solution when some reasonable...

34C37 | 35B38 | 35A15 | singular differential equations | periodic solutions | Mathematics | variational methods | damped | Ordinary Differential Equations | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Partial Differential Equations | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | SYSTEMS | FIXED-POINT THEOREM | Research | Periodic functions | Mathematical research | Calculus of variations | Differential equations | Mathematical analysis | Boundary value problems

34C37 | 35B38 | 35A15 | singular differential equations | periodic solutions | Mathematics | variational methods | damped | Ordinary Differential Equations | Analysis | Difference and Functional Equations | Approximations and Expansions | Mathematics, general | Partial Differential Equations | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | SYSTEMS | FIXED-POINT THEOREM | Research | Periodic functions | Mathematical research | Calculus of variations | Differential equations | Mathematical analysis | Boundary value problems

Journal Article

Optical and Quantum Electronics, ISSN 0306-8919, 3/2019, Volume 51, Issue 3, pp. 1 - 13

In this paper, the quintic derivative nonlinear Schrödinger equation is investigated into two main aspects. Firstly, a series of solutions of this equation are...

The explicit power series solutions | Optics, Lasers, Photonics, Optical Devices | Characterization and Evaluation of Materials | Dark solitons | Stability analysis | The quintic derivative nonlinear Schrödinger equation | Computer Communication Networks | Physics | Singular solitons | Electrical Engineering | RATIONAL SOLUTIONS | TRAVELING-WAVE SOLUTIONS | QUANTUM SCIENCE & TECHNOLOGY | The quintic derivative nonlinear Schrodinger equation | OPTICS | ENGINEERING, ELECTRICAL & ELECTRONIC

The explicit power series solutions | Optics, Lasers, Photonics, Optical Devices | Characterization and Evaluation of Materials | Dark solitons | Stability analysis | The quintic derivative nonlinear Schrödinger equation | Computer Communication Networks | Physics | Singular solitons | Electrical Engineering | RATIONAL SOLUTIONS | TRAVELING-WAVE SOLUTIONS | QUANTUM SCIENCE & TECHNOLOGY | The quintic derivative nonlinear Schrodinger equation | OPTICS | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

Computational and Applied Mathematics, ISSN 0101-8205, 7/2018, Volume 37, Issue 3, pp. 3806 - 3812

In this paper, we show that a proper limit of solutions of discrete Hamilton–Jacobi–Bellman (dHJB) equations in a random walk model becomes a viscosity...

Discrete Hamilton–Jacobi–Bellman equation | Computational Mathematics and Numerical Analysis | 93E20 | 91G10 | Mathematical Applications in Computer Science | Viscosity solution | Hamilton–Jacobi–Bellman variational inequality | Mathematics | Applications of Mathematics | Singular stochastic control problem | Mathematical Applications in the Physical Sciences | 91G80 | MATHEMATICS, APPLIED | Discrete Hamilton-Jacobi-Bellman equation | Hamilton-Jacobi-Bellman variational inequality

Discrete Hamilton–Jacobi–Bellman equation | Computational Mathematics and Numerical Analysis | 93E20 | 91G10 | Mathematical Applications in Computer Science | Viscosity solution | Hamilton–Jacobi–Bellman variational inequality | Mathematics | Applications of Mathematics | Singular stochastic control problem | Mathematical Applications in the Physical Sciences | 91G80 | MATHEMATICS, APPLIED | Discrete Hamilton-Jacobi-Bellman equation | Hamilton-Jacobi-Bellman variational inequality

Journal Article

理论物理通讯：英文版, ISSN 0253-6102, 2014, Volume 61, Issue 4, pp. 415 - 422

In the paper two kinds of solutions are derived for the complex Korteweg-de Vries equation, includ- ing blow-up solutions and non-singular solutions. We derive...

溶液 | 非奇异解 | 孤子解 | 公式 | 德弗里斯 | 爆破解 | 方程 | Miura变换 | non-singular solutions | complex Korteweg-de Vries equation | blow-up | DISSIPATION | PHYSICS, MULTIDISCIPLINARY | DYNAMICS | KDV EQUATION

溶液 | 非奇异解 | 孤子解 | 公式 | 德弗里斯 | 爆破解 | 方程 | Miura变换 | non-singular solutions | complex Korteweg-de Vries equation | blow-up | DISSIPATION | PHYSICS, MULTIDISCIPLINARY | DYNAMICS | KDV EQUATION

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2010, Volume 371, Issue 1, pp. 57 - 68

In this paper, we investigate the existence of positive solutions for the singular fractional boundary value problem: D α u ( t ) + f ( t , u ( t ) , D μ u ( t...

Fractional differential equation | Singular Dirichlet problem | Riemann–Liouville fractional derivative | Positive solution | Riemann-Liouville fractional derivative | MATHEMATICS | ORDER | MATHEMATICS, APPLIED | BOUNDARY-VALUE PROBLEM

Fractional differential equation | Singular Dirichlet problem | Riemann–Liouville fractional derivative | Positive solution | Riemann-Liouville fractional derivative | MATHEMATICS | ORDER | MATHEMATICS, APPLIED | BOUNDARY-VALUE PROBLEM

Journal Article

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 11/2013, Volume 88, Issue 5, p. 052113

We consider the Bethe equations for the isotropic spin-1/2 Heisenberg quantum spin chain with periodic boundary conditions. We formulate a conjecture for the...

XXZ CHAIN | INVARIANCE | POLYNOMIAL SYSTEMS | NONLINEAR ANALYTIC SYSTEMS | PHYSICS, FLUIDS & PLASMAS | SPIN CHAIN | COMPUTING SINGULAR SOLUTIONS | HOMOTOPY CONTINUATION | PHYSICS, MATHEMATICAL | HEISENBERG-MODEL | ANSATZ SOLUTIONS | PATH TRACKING

XXZ CHAIN | INVARIANCE | POLYNOMIAL SYSTEMS | NONLINEAR ANALYTIC SYSTEMS | PHYSICS, FLUIDS & PLASMAS | SPIN CHAIN | COMPUTING SINGULAR SOLUTIONS | HOMOTOPY CONTINUATION | PHYSICS, MATHEMATICAL | HEISENBERG-MODEL | ANSATZ SOLUTIONS | PATH TRACKING

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