高阶Chen-Lee-Liu方程在半直线上的初边值问题

Abstract

Abstract:

In this paper, the initial-boundary value problems of the higher-order Chen-Lee-Liu (HOCLL) equation on the half-line has been analysed via the Fokas method. We show that the solution q(x, t) of HOCLL equation can be expressed in terms of the unique solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter λ.

Key words: Riemann-Hilbert problem, Higher-order Chen-Lee-Liu equation, Jump matrix, Fokas method

CLC Number:

O175

Beibei Hu,Ling Zhang,Ning Zhang. An Initial-Boundary Value Problem for the Higher-Order Chen-Lee-Liu Equation on the Half-Line[J].Acta mathematica scientia,Series A, 2020, 40(2): 422-431.

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References 30

1	Fokas A S . A unified transform method for solving linear and certain nonlinear PDEs. Proc R Soc Lond A, 1997, 453, 1411- 1443
2	Fokas A S . Integrable nonlinear evolution equations on the half-line. Commun Math Phys, 2002, 230, 1- 39
3	Lenells J . The derivative nonlinear Schrödinger equation on the half-line. Phys D, 2008, 237, 3008- 3019
4	Zhang N , Xia T C , Fan E G . A Riemann-Hilbert approach to the Chen-Lee-Liu equation on the half line. Acta Math Applicatae Sin-E, 2018, 34 (3): 493- 515
5	Zhang N , Xia T C , Hu B B . A Riemann-Hilbert approach to the complex Sharma-Tasso-Olver equation on the half line. Commun Theor Phys, 2017, 68, 580- 594
6	Lenells J . Initial-boundary value problems for integrable evolution equations with 3×3 Lax pairs. Phys D, 2012, 241, 857- 875
7	Lenells J . The Degasperis-Procesi equation on the half-line. Nonlinear Anal, 2013, 76, 122- 139
8	Xu J , Fan E G . The three wave equation on the half-line. Phys Lett A, 2014, 378, 26- 33
9	Xu J , Fan E G . A Riemann-Hilbert approach to the initial-boundary problem for derivative nonlinear Schrödinger equation. Acta Math Sci, 2014, 34B, 973- 994
10	Xiao Y , Fan E G , Xu J . The Fokas-Lenells equation on the finite interval. Acta Math Sci, 2017, 37B, 852- 876
11	Boutet de Monvel A , Shepelsky D , Zielinski L . A Riemann-Hilbert approach for the Novikov equation. SIGMA, 2016, 12, 095
12	Tian S F . The mixed coupled nonlinear Schrödinger equation on the half-line via the Fokas method. Proc R Soc A, 2016, 472, 1- 22
13	Tian S F . Initial-boundary value problems of the coupled modified Korteweg-de Vries equation on the half-line via the Fokas method. J Phys A Math Theor, 2017, 50, 395204
14	Tian S F . Initial-boundary value problems for the general coupled nonlinear Schrödinger equation on the interval via the Fokas method. J Differ Equations, 2017, 262, 506- 558
15	Yan Z Y . An initial-boundary value problem for the integrable spin-1 Gross-Pitaevskii equations with a 4×4 Lax pair on the half-line. CHAOS, 2017, 27, 053117
16	Zhang N , Xia T C , Hu B B . A Riemann-Hilbert approach to the complex Sharma-Tasso-Olver equation on the half Line. Commun Theor Phys, 2017, 68, 580- 594
17	Hu B B , Xia T C , Zhang N , Wang J B . Initial-boundary value problems for the coupled higher-order nonlinear Schrödinger equations on the half-line. Int J Nonlin Sci Num, 2018, 19, 83- 92
18	Hu B B , Xia T C , Ma W X . Riemann-Hilbert approach for an initial-boundary value problem of the two-component modified Korteweg-de Vries equation on the half-line. Appl Math Comput, 2018, 332, 148- 159
19	Hu B B , Xia T C . A Fokas approach to the coupled modified nonlinear Schrödinger equation on the half-line. Math Meth Appl Sci, 2018, 41, 5112- 5123
20	Hu B B , Xia T C , Ma W X . Riemann-Hilbert approach for an initial-boundary value problem of an integrable coherently coupled nonlinear Schrödinger system on the half-line. E Asian J Appld Math, 2018, 8, 531- 548
21	Hu B B , Xia T C , Zhang N . The unified transform method to initial-boundary value problem of the coupled cubic-quintic nonlinear Schrödinger system. Complex Anal Oper Th, 2019, 13, 1143- 1159
22	Hu B B , Xia T C . A Riemann-Hilbert approach to the initial-boundary value problem for Kundu-Eckhaus equation on the half line. Complex Var Elliptic, 2019, 64 (12): 2019- 2039
23	董凤娇, 胡贝贝. 广义Sasa-Satsuma方程在半直线上的初边值问题. 华东师范大学学报(自然科学版), 2019, 4 (1): 33- 41
	Dong F J , Hu B B . An initial-boundary value problem for the generalized Sasa-Satsuma equation on the half-line. Journal of East China Normal University (Natural Science), 2019, 4, 33- 41
24	Ma W X . Riemann-Hilbert problems and N-soliton solutions for a coupled mKdV system. J Geom Phys, 2018, 132, 45- 54
25	Ma W X . Riemann-Hilbert problems of a six-component fourth-order AKNS system and its soliton solutions. Comput Appl Math, 2018, 37, 6359- 6375
26	Ma W X . Application of the Riemann-Hilbert approach to the multicomponent AKNS integrable hierarchies. Nonlinear Anal Real, 2019, 47, 1- 17
27	Ma W X . Riemann-Hilbert problems and soliton solutions of a multicomponent mKdV system and its reduction. Math Meth Appl Sci, 2019, 42, 1099- 1113
28	Ma W X . Riemann-Hilbert problems of a six-component mKdV system and its soliton solutions. Acta Math Sci, 2019, 39, 509- 523
29	Hu J , Xu J , Yu G F . Riemann-Hilbert approach and N-soliton formula for a higher-order Chen-Lee-Liu equation. J Nonlinear Math Phy, 2018, 25 (4): 633- 649
30	Zhang J , Liu W , Qiu D Q , et al. Rogue wave solutions of a higher-order Chen-Lee-Liu equation. Phys Scr, 2015, 90, 055207

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An Initial-Boundary Value Problem for the Higher-Order Chen-Lee-Liu Equation on the Half-Line

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