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Optik - International Journal for Light and Electron Optics, ISSN 0030-4026, 06/2016, Volume 127, Issue 12, pp. 4970 - 4983
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
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
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
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
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
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 2008, Volume 204, Issue 2, pp. 817 - 823
Journal Article
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 06/2018, Volume 41, Issue 9, pp. 3430 - 3440
Journal Article
Boundary Value Problems, ISSN 1687-2762, 12/2015, Volume 2015, Issue 1, pp. 1 - 11
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
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
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
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
Journal Article