The Riemann—Hilbert problem to coupled nonlinear Schrödinger equation: Long-time dynamics on the half-line

被引：0
作者：
Boling Guo
Nan Liu
机构：
[1] Institute of Applied Physics and Computational Mathematics,
来源：
Journal of Nonlinear Mathematical Physics | 2019年 / 26卷
关键词：
Coupled nonlinear Schrödinger equation; Riemann—Hilbert problem; Initial-boundary value problem; Long-time asymptotics; 35K20; 37K40; 35Q15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We derive the long-time asymptotics for the solution of initial-boundary value problem of coupled nonlinear Schrödinger equation whose Lax pair involves 3 × 3 matrix in present paper. Based on a nonlinear steepest descent analysis of an associated 3 × 3 matrix Riemann—Hilbert problem, we can give the precise asymptotic formulas for the solution of the coupled nonlinear Schrödinger equation on the half-line.
引用
收藏
页码：483 / 508
页数：25
相关论文
共 44 条
  • [1] Arruda LK(2017)Long-time asymptotics for the derivative nonlinear Schrödinger equation on the half-line Nonlinearity 30 4141-4172
  • [2] Lenells J(2017)Long-time asymptotics for the focusing nonlinear Schrödinger equation with nonzero boundary conditions at infinity and asymptotic stage of modulational instability, Commun. Pure Appl Math. 70 2300-2365
  • [3] Biondini G(2009)Long-time asymptotics for the focusing NLS equation with time-periodic boundary condition on the half-line, Commun Math. Phys. 290 479-522
  • [4] Mantzavinos D(2011)equation: Long-time dynamics of step-like initial data Int. Math. Res. Not. 2011 1613-1653
  • [5] Boutet de Monvel A(2013)A Riemann–Hilbert approach for the Degasperis–Procesi equation Nonlinearity 26 2081-2107
  • [6] Its A(2017)The short pulse equation by a Riemann–Hilbert approach, Lett Math. Phys. 107 1345-1373
  • [7] Kotlyarov V(2007)Long-time asymptotics of the nonlinear Schrödinger equation shock problem, Commun. Pure Appl Math. 60 1349-1414
  • [8] Boutet de Monvel A(1999)Uniform asymptotics for polynomials orthogonal with respect to varying exponential weights and applications to universality questions in random matrix theory, Commun. Pure Appl Math. 52 1335-1425
  • [9] Kotlyarov V(1993)A steepest descent method for oscillatory Riemann–Hilbert problems. Asymptotics for the MKdV equation Ann. Math. 137 295-368
  • [10] Shepelsky D(1997)A unified transform method for solving linear and certain nonlinear PDEs Proc. R. Soc. Lond. A 453 1411-1443
12345