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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
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
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
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
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
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
Journal Article
Nonlinear Dynamics, ISSN 0924-090X, 10/2017, Volume 90, Issue 1, pp. 363 - 369
Journal Article
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
Journal Article
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
Journal Article
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
Journal Article
Nonlinear Dynamics, ISSN 0924-090X, 9/2019, Volume 97, Issue 4, pp. 2127 - 2134
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
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
Journal Article
The Annals of Applied Probability, ISSN 1050-5164, 4/2014, Volume 24, Issue 2, pp. 616 - 651
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
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
Journal Article
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