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Chaos: An Interdisciplinary Journal of Nonlinear Science, ISSN 1054-1500, 08/2016, Volume 26, Issue 8, p. 084312
This paper investigates the Korteweg-de Vries equation within the scope of the local fractional derivative formulation. The exact traveling wave solutions of... 
PHYSICS, MATHEMATICAL | MATHEMATICS, APPLIED
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 12/2019, Volume 267, Issue 12, pp. 6872 - 6909
Averaging principle is a powerful tool for studying qualitative analysis of nonlinear dynamical systems. In this paper, we will establish an averaging... 
Stochastic Korteweg-de Vries equation | Averaging principle | MATHEMATICS | SYSTEMS | DIFFUSION-EQUATIONS
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 01/2017, Volume 42, pp. 699 - 708
Very recently, Ablowitz and Musslimani introduced a new integrable nonlocal nonlinear Schrödinger equation. In this paper, we investigate an integrable... 
Soliton solutions | Integrability | Nonlocal modified Korteweg-de Vries equation | Darboux transformation | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PLASMA | SYMMETRY | PHYSICS, FLUIDS & PLASMAS | PHYSICS, MATHEMATICAL
Journal Article
Journal of Mathematical Physics, ISSN 0022-2488, 05/2019, Volume 60, Issue 5, p. 51507
The initial-boundary value problem (IBVP) for the Korteweg-de Vries (KdV) equation on an interval is studied by extending a novel approach recently developed... 
EVOLUTION | DEVRIES EQUATION | TRANSFORM METHOD | BOUNDARY-VALUE-PROBLEM | ILL-POSEDNESS | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | GLOBAL WELL-POSEDNESS | Boundary value problems | Solution space | Cauchy problems | Sobolev space | Well posed problems | Iterative methods | Formulas (mathematics) | Cauchy problem
Journal Article
PHYSICS LETTERS A, ISSN 0375-9601, 05/2019, Volume 383, Issue 15, pp. 1689 - 1697
This paper is concerned with a negative order modified Korteweg-de Vries (nmKdV) equation which is in the negative flow of the mKdV hierarchy. We construct the... 
Nonlinear stability | STATES | EVOLUTION | Breather solutions | PHYSICS, MULTIDISCIPLINARY | Negative order mKdV equation | HIERARCHIES | Lyapunov function | Environmental law
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 06/2014, Volume 89, Issue 6, p. 062917
In this paper, we consider the complex modified Korteweg-de Vries (mKdV) equation as a model of few-cycle optical pulses. Using the Lax pair, we construct a... 
FIBERS | SOLITONS | PLASMA | PHYSICS, FLUIDS & PLASMAS | DISPERSION | SYSTEMS | MEDIA | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL | MODULATION | Models, Theoretical | Quantum Theory | Electromagnetic Radiation | Nonlinear Dynamics | Optics and Photonics | Computer Simulation
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 02/2020, Volume 100, p. 106043
A nonlocal 2-component complex modified Korteweg–de Vries equation will be investigated in this paper. We derive the -fold Darboux transformation in the form... 
Soliton solution | Periodic background | Nonlocal 2-component complex modified Korteweg–de Vries equation | Darboux transformation
Journal Article
IEEE Transactions on Automatic Control, ISSN 0018-9286, 07/2013, Volume 58, Issue 7, pp. 1688 - 1695
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 09/2018, Volume 332, pp. 148 - 159
In this work, we investigate the two-component modified Korteweg-de Vries (mKdV) equation, which is a complete integrable system, and accepts a generalization... 
Initial-boundary value problem | Unified transform method | Two-component mKdV equation | Riemann–Hilbert problem | MATHEMATICS, APPLIED | Riemann-Hilbert problem | SOLITON-SOLUTIONS | EVOLUTION-EQUATIONS | NONLINEAR SCHRODINGER-EQUATION | KDV
Journal Article
Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 11/1995, Volume 12, Issue 6, pp. 673 - 725
This paper is concerned with regularizing effects of solutions to the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations in one space... 
ANALYTICITY | MATHEMATICS, APPLIED | DISPERSIVE EQUATIONS | DEVRIES EQUATION
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 10/2017, Volume 310, pp. 97 - 111
This paper considers the stochastic Korteweg–de Vries equation on a bounded domain. The existence of a weak martingale solution is discussed by the Galerkin’s... 
Stochastic Korteweg–de Vries equation | Unique Continuation Property | Weak martingale solution | MATHEMATICS, APPLIED | SOLITONS | DECAY | KDV EQUATION | DRIVEN | Stochastic Korteweg-de Vries equation | CONTROLLABILITY
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 12/2017, Volume 53, pp. 83 - 93
The inverse scattering transform of the coupled modified Korteweg–de Vries equation is studied by the Riemann–Hilbert approach. In the direct scattering... 
Inverse scattering transform | Coupled mKdV equation | Multi-soliton solution | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | PHYSICS, FLUIDS & PLASMAS | KDV | PHYSICS, MATHEMATICAL
Journal Article
Physics Letters A, ISSN 0375-9601, 2002, Volume 301, Issue 1, pp. 35 - 44
A novel class of explicit exact solutions to the Korteweg-de Vries equation is presented through its bilinear form. Such solutions possess singularities of... 
Wronskian determinants | Positons | KdV equation | Complexitons | Schrödinger spectral problem | Solitons | DEVRIES | complexitons | SOLITON-SOLUTIONS | LINEAR EVOLUTION EQUATIONS | PHYSICS, MULTIDISCIPLINARY | positons | Schrodinger spectral problem | solitons | KDV HIERARCHY
Journal Article
Communications in Theoretical Physics, ISSN 0253-6102, 05/2019, Volume 71, Issue 5, pp. 489 - 495
Starting from the truncated Painleve expansion, the residual symmetry of the Alice-Bob modified Kortewegde Vries (AB-mKdV) equation is derived. The residual... 
explicit solution | Backlund transformation | residual symmetry | Alice-Bob modified Korteweg-de Vries equation | symmetry | PHYSICS, MULTIDISCIPLINARY | SIMILARITY REDUCTIONS | SOLVABILITY | PsTd symmetry | NONLOCAL SYMMETRY
Journal Article
Journal of Optimization Theory and Applications, ISSN 0022-3239, 1/2019, Volume 180, Issue 1, pp. 290 - 302
The initial and initial-boundary value problems, posed on infinite domains for Korteweg–de Vries equation, are considered. The right-hand side of the equation... 
Korteweg–de Vries equation | Mathematics | Theory of Computation | 35Q53 | Optimization | 35Q93 | Integral condition | Control | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Initial-boundary value problem | Applications of Mathematics | Engineering, general | 49N45 | Integrals | Boundary value problems
Journal Article
SIAM Journal on Control and Optimization, ISSN 0363-0129, 2017, Volume 55, Issue 6, pp. 3503 - 3532
In this paper we study boundary controllability of the Korteweg-de Vries equation posed on a finite domain with the Neumann boundary conditions. We consider... 
Korteweg-de Vries equation | Exact boundary controllability | Critical set | Dirichlet boundary conditions | Neumann boundary conditions | exact boundary controllability | MATHEMATICS, APPLIED | STABILIZATION | PERIODIC DOMAIN | LINEAR KDV EQUATION | FLUID | critical set | FINITE DOMAIN | STABILIZABILITY | AUTOMATION & CONTROL SYSTEMS
Journal Article
Chaos: An Interdisciplinary Journal of Nonlinear Science, ISSN 1054-1500, 01/2019, Volume 29, Issue 1, p. 013117
We revise the solutions of the forced Korteweg–de Vries equation describing a resonant interaction of a solitary wave with external pulse-type perturbations.... 
WAVE | MATHEMATICS, APPLIED | FLUID | RESONANT FLOW | GENERATION | PHYSICS, MATHEMATICAL | LONG | Physics - Pattern Formation and Solitons
Journal Article
Journal of Geometry and Physics, ISSN 0393-0440, 08/2019, Volume 142, pp. 151 - 167
On the basis of the inverse scattering transformation, the Cauchy problem of the coupled modified Korteweg–de Vries equation is transformed to a 3 × 3 matrix... 
Long-time asymptotics | Coupled modified Korteweg–de Vries equation | Nonlinear steepest descent method | MATHEMATICS | STEEPEST DESCENT METHOD | WAVES | SOLITON-SOLUTIONS | INVERSE SCATTERING TRANSFORM | Coupled modified Korteweg-de Vries equation | RIEMANN-HILBERT PROBLEMS | NONLINEAR SCHRODINGER-EQUATION | PHYSICS, MATHEMATICAL
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 11/2017, Volume 73, pp. 136 - 142
The residual symmetry is derived for the negative-order Korteweg–de Vries equation from the truncated Painlevé expansion. This nonlocal symmetry is transformed... 
Residual symmetry | Soliton-cnoidal wave interaction solution | Consistent tanh expansion method | [formula omitted]th bäcklund transformation | Negative-order KdV equation | MATHEMATICS, APPLIED | PARTIAL-DIFFERENTIAL-EQUATIONS | EVOLUTION-EQUATIONS | PAINLEVE | nth backlund transformation | Differential equations
Journal Article
Complexity, ISSN 1076-2787, 10/2019, Volume 2019, pp. 1 - 10
The residual symmetry of a negative-order Korteweg–de Vries (nKdV) equation is derived through its Lax pair. Such residual symmetry can be localized, and the... 
Journal Article
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