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Long-time asymptotics of the focusing Kundu–Eckhaus equation with nonzero boundary conditions
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In this article, the authors investigated the long-time asymptotics of the focusing Kundu-Eckhaus equation with nonzero boundary conditions at infinity by the nonlinear steepest descent method of Deift and Zhou.About:
This article is published in Journal of Differential Equations.The article was published on 2019-04-15. It has received 180 citations till now. The article focuses on the topics: Boundary value problem & Plane wave.read more
Citations
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Riemann–Hilbert method and multi-soliton solutions for three-component coupled nonlinear Schrödinger equations
TL;DR: In this paper, an integrable three-component coupled nonlinear Schrodinger (NLS) equation is considered and the scattering and inverse scattering problems of the NLS equation by using the Riemann-Hilbert formulation are presented.
Journal ArticleDOI
Symmetric and Anti-Symmetric Solitons of the Fractional Second- and Third-Order Nonlinear Schrödinger Equation
Qi-Hao Cao,Chao-Qing Dai +1 more
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Different wave structures and stability analysis for the generalized (2+1)-dimensional Camassa-Holm-Kadomtsev-Petviashvili equation
TL;DR: In this article, the generalized (2+1)-dimensional Camassa-Holm-Kadomtsev-Petviashvili (2D-gCHKP) equation describing the dispersion role in the formation of patterns in liquid drops is studied.
Journal ArticleDOI
Consistent Riccati expansion and rational solutions of the Drinfel’d–Sokolov–Wilson equation
Bo Ren,Ji Lin,Zhi-Mei Lou +2 more
TL;DR: The consistent Riccati expansion is used to the Drinfel’d–Sokolov–Wilson (DSW) equation and it is demonstrated that the DSW equation is the CRE solvability system.
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Mixed lump and soliton solutions for a generalized (3+1)-dimensional Kadomtsev-Petviashvili equation
Yu-Lan Ma,Bang-Qing Li +1 more
TL;DR: In this article, a generalized (3+1)-dimensional Kadomtsev-Petviashvili equation is used to describe nonlinear wave propagation in dissipative media.
References
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Journal ArticleDOI
Method for solving the Korteweg-deVries equation
TL;DR: In this paper, a method for solving the initial value problem of the Korteweg-deVries equation is presented which is applicable to initial data that approach a constant sufficiently rapidly as
Journal ArticleDOI
The disintegration of wave trains on deep water Part 1. Theory
T. Brooke Benjamin,J. E. Feir +1 more
TL;DR: In this paper, a theoretical analysis of the stability of periodic wave trains to small disturbances in the form of a pair of side-band modes is presented, where the wave train becomes highly irregular far from its origin, even when the departures from periodicity are scarcely detectable at the start.
Book
Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach
TL;DR: In this paper, the authors present an asymptotics for orthogonal polynomials in Riemann-Hilbert problems and Jacobi operators for continued fractions.
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A steepest descent method for oscillatory Riemann–Hilbert problems. Asymptotics for the MKdV equation
Percy Deift,Xin Zhou +1 more
TL;DR: In this article, the authors present an approach to analyze the asymptotics of oscillatory Riemann-Hilbert problems with respect to the modified Korteweg-de Vries (MKdV) equation.