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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
Journal of Differential Equations, ISSN 0022-0396, 01/2017, Volume 262, Issue 1, pp. 506 - 558
Journal Article
2016, Graduate studies in mathematics, ISBN 1470430959, Volume 177, xxiii, 275 pages
Book
Applied Mathematics Letters, ISSN 0893-9659, 09/2019, Volume 95, pp. 65 - 71
The matrix Riemann–Hilbert problem of the Hirota equation with non-zero boundary conditions is investigated. Based on the matrix Riemann–Hilbert problem, the... 
Darboux transform | Rogue waves | Hirota equation | Non-zero boundary conditions | Riemann–Hilbert problem | Breathers | MATHEMATICS, APPLIED | Riemann-Hilbert problem | Water waves
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 01/2019, Volume 87, pp. 57 - 63
The solution of the initial value problem (IVP) for the Fokas–Lenells equation (FLE) was constructed in terms of the solution M(x,t,k) of a 2 × 2 matrix... 
Fokas–Lenells equation | Initial value problem | Negative order Lax pair | Riemann–Hilbert problem | MATHEMATICS, APPLIED | Riemann-Hilbert problem | SOLITONS | Fokas-Lenells equation
Journal Article
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, ISSN 1364-5021, 11/2016, Volume 472, Issue 2195, p. 20160588
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 08/2015, Volume 259, Issue 3, pp. 1098 - 1148
We use the Deift–Zhou method to obtain, in the solitonless sector, the leading order asymptotic of the solution to the Cauchy problem of the Fokas–Lenells... 
Deift–Zhou method | Fokas–Lenells equation | Initial value problem | Riemann–Hilbert problem | Riemann-Hilbert problem | Fokas-Lenells equation | Deift-Zhou method | MATHEMATICS | NONLINEAR SCHRODINGER-EQUATION
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 10/2016, Volume 333, pp. 171 - 184
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 02/2018, Volume 76, pp. 81 - 89
We present a Riemann–Hilbert problem formalism for the initial value problem of the Kundu–Eckhaus equation on the line. The long-time asymptotic for the... 
Deift–Zhou nonlinear steepest descent method | Long-time asymptotic | Kundu–Eckhaus equation | Initial value problem | Riemann–Hilbert problem | Deift-Zhou nonlinear steepest descent method | MATHEMATICS, APPLIED | Riemann-Hilbert problem | SOLITONS | Kundu-Eckhaus equation | NONLINEAR SCHRODINGER-EQUATION
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2017, Volume 448, Issue 2, pp. 864 - 884
A complex harmonic function of finite Dirichlet energy on a Jordan domain has boundary values in a certain conformally invariant sense, by a construction of H.... 
Dirichlet space | Quasidisks | Limiting Cauchy integral | Harmonic reflection | Riemann–Hilbert problem | MATHEMATICS | MATHEMATICS, APPLIED | Riemann-Hilbert problem | THEOREM | Naturvetenskap | Matematisk analys | Mathematics | Natural Sciences | Matematik | Mathematical Analysis
Journal Article
Applied Mathematics Letters, ISSN 0893-9659, 08/2019, Volume 94, pp. 8 - 12
The short pulse equation is an important integrable equation, which can be solved by the so-called inverse scattering method with the help of a... 
Short pulse equation | Linear initial value | Box-like initial value | Riemann–Hilbert problem | MATHEMATICS, APPLIED | Riemann-Hilbert problem | LONG-TIME ASYMPTOTICS | RIEMANN-HILBERT PROBLEMS
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 02/2018, Volume 364, pp. 27 - 61
Journal Article
Zeitschrift für Naturforschung A, ISSN 0932-0784, 01/2019, Volume 74, Issue 2, pp. 139 - 145
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2016, Volume 443, Issue 2, pp. 797 - 816
In this paper a theory is developed for obtaining families of solutions to the KdV equation by formulating a Riemann–Hilbert problem with an appropriate shift.... 
Factorization | Integrable systems | Riemann–Hilbert problems | Riemann-Hilbert problems | MATHEMATICS | MATHEMATICS, APPLIED | DE-VRIES EQUATION | Analysis | Numerical analysis
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 06/2020, Volume 268, Issue 12, pp. 7480 - 7504
We consider the initial-value problem for the Sasa–Satsuma equation on the line with decaying initial data. Using a Riemann–Hilbert formulation and steepest... 
Sasa–Satsuma equation | Asymptotics | Initial value problem | Riemann–Hilbert problem | MATHEMATICS | Riemann-Hilbert problem | STEEPEST DESCENT METHOD | RIEMANN-HILBERT PROBLEMS | Sasa-Satsuma equation
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2019, Volume 2019, Issue 1, pp. 1 - 19
Journal Article
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