Mathematische Annalen, ISSN 0025-5831, 4/2016, Volume 364, Issue 3, pp. 777 - 792

We show that expanding Kähler–Ricci solitons which have positive holomorphic bisectional curvature and are $$C^{2}$$ C 2 -asymptotic to a conical Kähler...

Mathematics, general | Secondary 35C08 | Mathematics | Primary 53C44

Mathematics, general | Secondary 35C08 | Mathematics | Primary 53C44

Journal Article

Journal of King Saud University - Science, ISSN 1018-3647, 10/2019, Volume 31, Issue 4, pp. 485 - 489

In this paper we introduce a new type of KdV equations called Two-mode KdV (TMKdV). This equation represents the propagation of two-wave modes in the same...

Jacobi elliptic function methods | Two-mode KdV equation | 74J35 | 35C08 | PERIODIC-SOLUTIONS | FUNCTION EXPANSION | STABILITY ANALYSIS | MULTIDISCIPLINARY SCIENCES | ZAKHAROV-KUZNETSOV EQUATION | SOLITARY WAVE SOLUTIONS

Jacobi elliptic function methods | Two-mode KdV equation | 74J35 | 35C08 | PERIODIC-SOLUTIONS | FUNCTION EXPANSION | STABILITY ANALYSIS | MULTIDISCIPLINARY SCIENCES | ZAKHAROV-KUZNETSOV EQUATION | SOLITARY WAVE SOLUTIONS

Journal Article

Journal of Interdisciplinary Mathematics, ISSN 0972-0502, 08/2019, Volume 22, Issue 6, pp. 849 - 861

In this present study, new sub-equation method is used to construct exact travelling wave solutions of the Cahn-Hilliard equation (CH). As a consequence, many...

83C15 | New sub-equation method | Cahn-Hilliard equation | 34G20 | Exact solutions | Nonlinear evolution equations | 35C08 | 35C07

83C15 | New sub-equation method | Cahn-Hilliard equation | 34G20 | Exact solutions | Nonlinear evolution equations | 35C08 | 35C07

Journal Article

NONLINEAR DYNAMICS, ISSN 0924-090X, 07/2019, Volume 97, Issue 1, pp. 571 - 582

This paper presents necessary and sufficient conditions for the existence of bright/dark solitary solutions in the Hodgkin-Huxley model. The second-order...

Hodgkin-Huxley model | MECHANICS | EXP-FUNCTION | Heteroclinic bifurcation | 35B32 | NEURONS | Generalized differential operator | Solitary solution | 35C08 | DESYNCHRONIZATION | ENGINEERING, MECHANICAL

Hodgkin-Huxley model | MECHANICS | EXP-FUNCTION | Heteroclinic bifurcation | 35B32 | NEURONS | Generalized differential operator | Solitary solution | 35C08 | DESYNCHRONIZATION | ENGINEERING, MECHANICAL

Journal Article

Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, 04/2017, Volume 24, Issue 2, pp. 210 - 223

We consider the Riemann-Hilbert method for initial problem of the vector Gerdjikov-Ivanov equation, and obtain the formula for its N-soliton solution, which is...

Riemann-Hilbert problem | soliton | 35C11 | vector Gerdjikov-Ivanov equation | asymptotic analysis | 35Q55 | 37K40 | 35C08 | Vector Gerdjikov-Ivanov equation | Soliton | Asymptotic analysis | Riemann–Hilbert problem | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL

Riemann-Hilbert problem | soliton | 35C11 | vector Gerdjikov-Ivanov equation | asymptotic analysis | 35Q55 | 37K40 | 35C08 | Vector Gerdjikov-Ivanov equation | Soliton | Asymptotic analysis | Riemann–Hilbert problem | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 4/2019, Volume 109, Issue 4, pp. 945 - 973

Rogue waves in the nonlocal $${\mathcal {PT}}$$ PT -symmetric nonlinear Schrödinger (NLS) equation are studied by Darboux transformation. Three types of rogue...

Geometry | Schur polynomials | 37K35 | Rogue waves | Nonlocal NLS equation | Theoretical, Mathematical and Computational Physics | Complex Systems | 35Q55 | Group Theory and Generalizations | Physics | 35C08 | Darboux transformation | SOLITON-SOLUTIONS | NLS EQUATION | DE-VRIES EQUATION | PHYSICS, MATHEMATICAL | Water waves

Geometry | Schur polynomials | 37K35 | Rogue waves | Nonlocal NLS equation | Theoretical, Mathematical and Computational Physics | Complex Systems | 35Q55 | Group Theory and Generalizations | Physics | 35C08 | Darboux transformation | SOLITON-SOLUTIONS | NLS EQUATION | DE-VRIES EQUATION | PHYSICS, MATHEMATICAL | Water waves

Journal Article

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New three-wave solutions for the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Nonlinear Dynamics, ISSN 0924-090X, 4/2017, Volume 88, Issue 1, pp. 655 - 661

Based on the extended three-wave approach and the Hirota’s bilinear method, the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation is investigated. With...

Hirota’s bilinear form | 68M07 | 33F10 | Boiti–Leon–Manna–Pempinelli equation | Classical Mechanics | Symbolic computation | 35C08 | Engineering | Vibration, Dynamical Systems, Control | Three-wave solutions | Extended three-wave approach | Automotive Engineering | Mechanical Engineering | TRAVELING-WAVE SOLUTIONS | MECHANICS | Hirota's bilinear form | Boiti-Leon-Manna-Pempinelli equation | MULTIPLE-SOLITON-SOLUTIONS | ENGINEERING, MECHANICAL | Medicine, Chinese | Nonlinear dynamics | Solitary waves

Hirota’s bilinear form | 68M07 | 33F10 | Boiti–Leon–Manna–Pempinelli equation | Classical Mechanics | Symbolic computation | 35C08 | Engineering | Vibration, Dynamical Systems, Control | Three-wave solutions | Extended three-wave approach | Automotive Engineering | Mechanical Engineering | TRAVELING-WAVE SOLUTIONS | MECHANICS | Hirota's bilinear form | Boiti-Leon-Manna-Pempinelli equation | MULTIPLE-SOLITON-SOLUTIONS | ENGINEERING, MECHANICAL | Medicine, Chinese | Nonlinear dynamics | Solitary waves

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 2/2018, Volume 91, Issue 3, pp. 1619 - 1626

In this paper, we establish a new nonlinear equation which is called the two-mode Korteweg–de Vries–Burgers equation (TMKdV–BE). The new equation describes the...

74J35 | Engineering | Vibration, Dynamical Systems, Control | Two-mode KdV–Burgers equation | Tanh–coth expansion method | Classical Mechanics | Simplified bilinear method | Automotive Engineering | Mechanical Engineering | 35C08 | MATHEMATICAL PHYSICS | MECHANICS | SOLITONS | Two-mode KdV-Burgers equation | SOLITARY WAVE SOLUTIONS | SYSTEMS | Tanh-coth expansion method | KDV EQUATION | EVOLUTION-EQUATIONS | ENGINEERING, MECHANICAL | Series (mathematics) | Nonlinear equations | Wave propagation | Burgers equation

74J35 | Engineering | Vibration, Dynamical Systems, Control | Two-mode KdV–Burgers equation | Tanh–coth expansion method | Classical Mechanics | Simplified bilinear method | Automotive Engineering | Mechanical Engineering | 35C08 | MATHEMATICAL PHYSICS | MECHANICS | SOLITONS | Two-mode KdV-Burgers equation | SOLITARY WAVE SOLUTIONS | SYSTEMS | Tanh-coth expansion method | KDV EQUATION | EVOLUTION-EQUATIONS | ENGINEERING, MECHANICAL | Series (mathematics) | Nonlinear equations | Wave propagation | Burgers equation

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 10/2017, Volume 90, Issue 1, pp. 363 - 369

Many important physical situations such as fluid flows, plasma physics and solid-state physics have been described by (3+1)-dimensional generalized shallow...

Engineering | Vibration, Dynamical Systems, Control | 68M07 | 33F10 | Auto-Bäcklund transformation | Periodic solitary wave solutions | Classical Mechanics | Automotive Engineering | Mechanical Engineering | Symbolic computation | Generalized shallow water equation | 35C08 | MECHANICS | SOLITONS | Auto-Backlund transformation | ENGINEERING, MECHANICAL | Plasma physics | Differential equations | Shallow water equations | Nonlinear equations | Solid state physics | Plasma (physics) | Solitary waves

Engineering | Vibration, Dynamical Systems, Control | 68M07 | 33F10 | Auto-Bäcklund transformation | Periodic solitary wave solutions | Classical Mechanics | Automotive Engineering | Mechanical Engineering | Symbolic computation | Generalized shallow water equation | 35C08 | MECHANICS | SOLITONS | Auto-Backlund transformation | ENGINEERING, MECHANICAL | Plasma physics | Differential equations | Shallow water equations | Nonlinear equations | Solid state physics | Plasma (physics) | Solitary waves

Journal Article

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Riemann-Hilbert approach and N-soliton formula for a higher-order Chen-Lee-Liu equation

Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, 10/2018, Volume 25, Issue 4, pp. 633 - 649

We consider a higher-order Chen-Lee-Liu (CLL) equation with third order dispersion and quintic nonlinearity terms. In the framework of the Riemann-Hilbert...

Higher-order Chen-Lee-Liu equation | Riemann-Hilbert method | N-soliton | 35C11 | 35Q55 | 37K40 | 35C08 | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | INTEGRABLE SYSTEMS

Higher-order Chen-Lee-Liu equation | Riemann-Hilbert method | N-soliton | 35C11 | 35Q55 | 37K40 | 35C08 | MATHEMATICS, APPLIED | PHYSICS, MATHEMATICAL | INTEGRABLE SYSTEMS

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 6/2015, Volume 105, Issue 6, pp. 853 - 891

The second-type derivative nonlinear Schrödinger (DNLSII) equation was introduced as an integrable model in 1979. Very recently, the DNLSII equation has been...

Theoretical, Mathematical and Computational Physics | 35C11 | breather solution | 35Q55 | self-steepening | 37K40 | Statistical Physics, Dynamical Systems and Complexity | Physics | 35C08 | Geometry | the second-type derivative nonlinear Schrödinger equation | Group Theory and Generalizations | 78A60 | rogue wave solution | Darboux transformation | PEREGRINE SOLITON | NLS EQUATION | EXPLICIT SOLUTIONS | DIFFERENTIAL-DIFFERENCE | the second-type derivative nonlinear Schrodinger equation | PHYSICS, MATHEMATICAL | WATER-WAVES | MULTISOLITON SOLUTIONS | ALFVEN WAVES | ROGUE WAVES SOLUTIONS | SELF-PHASE MODULATION | PARALLEL

Theoretical, Mathematical and Computational Physics | 35C11 | breather solution | 35Q55 | self-steepening | 37K40 | Statistical Physics, Dynamical Systems and Complexity | Physics | 35C08 | Geometry | the second-type derivative nonlinear Schrödinger equation | Group Theory and Generalizations | 78A60 | rogue wave solution | Darboux transformation | PEREGRINE SOLITON | NLS EQUATION | EXPLICIT SOLUTIONS | DIFFERENTIAL-DIFFERENCE | the second-type derivative nonlinear Schrodinger equation | PHYSICS, MATHEMATICAL | WATER-WAVES | MULTISOLITON SOLUTIONS | ALFVEN WAVES | ROGUE WAVES SOLUTIONS | SELF-PHASE MODULATION | PARALLEL

Journal Article

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Soliton solutions and their (in)stability for the focusing Davey-Stewartson II equation

Nonlinearity, ISSN 0951-7715, 08/2018, Volume 31, Issue 9, pp. 4290 - 4325

We give a rigorous mathematical analysis of the one-soliton solution of the focusing Davey-Stewartson II equation and a proof of its instability under...

inverse scattering | Davey-Stewartson equation | Solitons | MATHEMATICS, APPLIED | INVERSE SCATTERING TRANSFORM | 37L50 | PHYSICS, MATHEMATICAL | 35C08 | Davey-Stewartson equation Mathematics Subject Classification numbers: 37K10 | EVOLUTION | NONLINEAR EQUATIONS | 35P25 | 35Q35 | SYSTEMS | 32W05 | BLOW-UP | PACKETS | solitons

inverse scattering | Davey-Stewartson equation | Solitons | MATHEMATICS, APPLIED | INVERSE SCATTERING TRANSFORM | 37L50 | PHYSICS, MATHEMATICAL | 35C08 | Davey-Stewartson equation Mathematics Subject Classification numbers: 37K10 | EVOLUTION | NONLINEAR EQUATIONS | 35P25 | 35Q35 | SYSTEMS | 32W05 | BLOW-UP | PACKETS | solitons

Journal Article

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A novel method for nonlinear fractional differential equations using symbolic computation

Waves in Random and Complex Media, ISSN 1745-5030, 01/2017, Volume 27, Issue 1, pp. 163 - 170

In this paper, a new approach, namely an ansatz method is applied to find exact solutions for nonlinear fractional differential equations in the sense of...

35Q68 | 35C08 | 34A08 | SOLITON-SOLUTIONS | EVOLUTION | 1ST INTEGRAL METHOD | PHYSICS, MULTIDISCIPLINARY | CALCULUS | WAVE SOLUTIONS | MODEL | DARK SOLITON | Ordinary differential equations | Partial differential equations | Exact solutions | Differential equations | Mathematical analysis | Nonlinearity | Mathematical models | Complex media | Transformations | Derivatives

35Q68 | 35C08 | 34A08 | SOLITON-SOLUTIONS | EVOLUTION | 1ST INTEGRAL METHOD | PHYSICS, MULTIDISCIPLINARY | CALCULUS | WAVE SOLUTIONS | MODEL | DARK SOLITON | Ordinary differential equations | Partial differential equations | Exact solutions | Differential equations | Mathematical analysis | Nonlinearity | Mathematical models | Complex media | Transformations | Derivatives

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 9/2019, Volume 97, Issue 4, pp. 2127 - 2134

Under investigation is a ( $$2 + 1$$ 2 + 1 )-dimensional variable-coefficient Korteweg–de Vries equation, which is used to describe the electrostatic wave...

68M07 | 33F10 | Lump–stripe | Classical Mechanics | Breather wave | Homoclinic breather approach | 35C08 | Engineering | Vibration, Dynamical Systems, Control | Multi-waves | Three waves method | Automotive Engineering | Mechanical Engineering | RATIONAL SOLUTIONS | MECHANICS | SOLITON-SOLUTIONS | Lump-stripe | BEHAVIOR | KDV EQUATION | DIVERSITY | ENGINEERING, MECHANICAL | Water waves | Artificial intelligence | Medicine, Chinese

68M07 | 33F10 | Lump–stripe | Classical Mechanics | Breather wave | Homoclinic breather approach | 35C08 | Engineering | Vibration, Dynamical Systems, Control | Multi-waves | Three waves method | Automotive Engineering | Mechanical Engineering | RATIONAL SOLUTIONS | MECHANICS | SOLITON-SOLUTIONS | Lump-stripe | BEHAVIOR | KDV EQUATION | DIVERSITY | ENGINEERING, MECHANICAL | Water waves | Artificial intelligence | Medicine, Chinese

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 4/2019, Volume 96, Issue 1, pp. 115 - 121

In this paper, we introduced a new dual-mode nonlinear Schrödinger (DMNLS) equation with nonlinearity Kerr of types square-root law and dual-power law. The new...

74J35 | Engineering | Vibration, Dynamical Systems, Control | Square-root Kerr | Classical Mechanics | Automotive Engineering | Dual-mode Schrödinger | Mechanical Engineering | Dual-power Kerr | Solitary wave solutions | 35C08 | MECHANICS | DARK | Dual-mode Schrodinger | EQUATION | ENGINEERING, MECHANICAL

74J35 | Engineering | Vibration, Dynamical Systems, Control | Square-root Kerr | Classical Mechanics | Automotive Engineering | Dual-mode Schrödinger | Mechanical Engineering | Dual-power Kerr | Solitary wave solutions | 35C08 | MECHANICS | DARK | Dual-mode Schrodinger | EQUATION | ENGINEERING, MECHANICAL

Journal Article

Frontiers of Mathematics in China, ISSN 1673-3452, 10/2019, Volume 14, Issue 5, pp. 1063 - 1075

A generalized Volterra lattice with a nonzero boundary condition is considered by virtue of the inverse scattering transform. The two-sheeted Riemann surface...

35P25 | Mathematics, general | Mathematics | Volterra lattice | inverse scattering transform | 35C08 | nonzero boundary condition | Boundary conditions | Riemann manifold | Riemann surfaces | Inverse scattering | Spectrum analysis | Volterra integral equations

35P25 | Mathematics, general | Mathematics | Volterra lattice | inverse scattering transform | 35C08 | nonzero boundary condition | Boundary conditions | Riemann manifold | Riemann surfaces | Inverse scattering | Spectrum analysis | Volterra integral equations

Journal Article

Nonlinear Dynamics, ISSN 0924-090X, 1/2018, Volume 91, Issue 1, pp. 497 - 504

Many important physical situations such as fluid flows, plasma physics, and solid-state physics have been described by the Korteweg–de Vries (KdV)-type models....

Hirota’s bilinear form | 68M07 | 33F10 | Classical Mechanics | KdV equation | Symbolic computation | 35C08 | Engineering | Vibration, Dynamical Systems, Control | Direct test function | Periodic solitary wave solutions | Automotive Engineering | Mechanical Engineering | SYSTEM | RATIONAL SOLUTIONS | MKDV EQUATION | 1-SOLITON SOLUTION | LAW NONLINEARITY | SHOCK-WAVES | ENGINEERING, MECHANICAL | MECHANICS | SOLITONS | EVOLUTION | Hirota's bilinear form | Plasma physics | Medicine, Chinese | Solid state physics | Nonlinear equations | Plasma (physics) | Solitary waves | Wave equations

Hirota’s bilinear form | 68M07 | 33F10 | Classical Mechanics | KdV equation | Symbolic computation | 35C08 | Engineering | Vibration, Dynamical Systems, Control | Direct test function | Periodic solitary wave solutions | Automotive Engineering | Mechanical Engineering | SYSTEM | RATIONAL SOLUTIONS | MKDV EQUATION | 1-SOLITON SOLUTION | LAW NONLINEARITY | SHOCK-WAVES | ENGINEERING, MECHANICAL | MECHANICS | SOLITONS | EVOLUTION | Hirota's bilinear form | Plasma physics | Medicine, Chinese | Solid state physics | Nonlinear equations | Plasma (physics) | Solitary waves | Wave equations

Journal Article

The Annals of Applied Probability, ISSN 1050-5164, 4/2014, Volume 24, Issue 2, pp. 616 - 651

We use the inverse scattering transform and a diffusion approximation limit theorem to study the stability of soliton components of the solution of the...

Determinism | Zero | Solitons | Differential equations | White noise | Cubes | Eigenvalues | Boundary conditions | Mathematical independent variables | Coefficients | NLS equation | Kdv equation | Random perturbation of initial conditions | Diffusion approximation limit theorem | KdV equation | STATISTICS & PROBABILITY | random perturbation of initial conditions | solitons | 60B12 | 35Q55 | 35Q53 | 35C08

Determinism | Zero | Solitons | Differential equations | White noise | Cubes | Eigenvalues | Boundary conditions | Mathematical independent variables | Coefficients | NLS equation | Kdv equation | Random perturbation of initial conditions | Diffusion approximation limit theorem | KdV equation | STATISTICS & PROBABILITY | random perturbation of initial conditions | solitons | 60B12 | 35Q55 | 35Q53 | 35C08

Journal Article

Advances in Difference Equations, ISSN 1687-1847, 12/2019, Volume 2019, Issue 1, pp. 1 - 8

Cross-soliton solution, breather soliton, periodic solitary solution, and doubly periodic solution are obtained by using an extended homoclinic test approach...

Retroflexion | Mathematics | 35C08 | 74J35 | Cross soliton | Degeneracy | Ordinary Differential Equations | Functional Analysis | YTSF equation | Analysis | Difference and Functional Equations | Mathematics, general | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | MULTISOLITON | WAVE SOLUTIONS | BIFURCATION | Perturbation methods | Nonlinear systems | Parameters

Retroflexion | Mathematics | 35C08 | 74J35 | Cross soliton | Degeneracy | Ordinary Differential Equations | Functional Analysis | YTSF equation | Analysis | Difference and Functional Equations | Mathematics, general | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | MULTISOLITON | WAVE SOLUTIONS | BIFURCATION | Perturbation methods | Nonlinear systems | Parameters

Journal Article

Zeitschrift für angewandte Mathematik und Physik, ISSN 0044-2275, 2/2020, Volume 71, Issue 1, pp. 1 - 23

We prove spatiotemporal algebraically decaying estimates for the density of the solutions of the linearly damped nonlinear Schrödinger equation with localized...

Damped and driven nonlinear Schrödinger equation | Rogue waves | 35Q55 | Algebraic decaying estimates | 37L50 | Theoretical and Applied Mechanics | 35C08 | Engineering | Mathematical Methods in Physics | 46E35 | Peregrine Soliton | 35B40 | Localized driver | Weighted Sobolev spaces

Damped and driven nonlinear Schrödinger equation | Rogue waves | 35Q55 | Algebraic decaying estimates | 37L50 | Theoretical and Applied Mechanics | 35C08 | Engineering | Mathematical Methods in Physics | 46E35 | Peregrine Soliton | 35B40 | Localized driver | Weighted Sobolev spaces

Journal Article

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