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pro vyhledávání: '"Zhang Da-jun"'
A reduction from the self-dual Yang-Mills (SDYM) equation to the unreduced Fokas-Lenells (FL) system is described in this paper. It has been known that the SDYM equation can be formulated from the Cauchy matrix schemes of the matrix Kadomtsev-Petvias
Externí odkaz:
http://arxiv.org/abs/2411.10807
In this paper the classical and nonlocal semi-discrete nonlinear Schr\"{o}dinger (sdNLS) equations with nonzero backgrounds are solved by means of the bilinearization-reduction approach. In the first step of this approach, the unreduced sdNLS system
Externí odkaz:
http://arxiv.org/abs/2409.01063
Autor:
Li, Shangshuai, Zhang, Da-jun
The paper establishes a direct linearization scheme for the SU(2) anti-self-dual Yang-Mills (ASDYM) equation.The scheme starts from a set of linear integral equations with general measures and plane wave factors. After introducing infinite-dimensiona
Externí odkaz:
http://arxiv.org/abs/2403.06055
In this paper, we show that all the bilinear Adler-Bobenko-Suris (ABS) equations (except Q2 and Q4) can be obtained from symmetric discrete AKP system by taking proper reductions and continuum limits. Among the bilinear ABS equations, a simpler bilin
Externí odkaz:
http://arxiv.org/abs/2312.15669
Autor:
Li, Xing, Zhang, Da-jun
The Lam\'e function can be used to construct plane wave factors and solutions to the Korteweg-de Vries (KdV) and Kadomtsev-Petviashvili (KP) hierarchy. The solutions are usually called elliptic solitons. In this chapter, first, we review recent devel
Externí odkaz:
http://arxiv.org/abs/2307.02312
In the recent paper [Stud. App. Math. 147 (2021) 752], squared eigenfunction symmetry constraint of the differential-difference modified Kadomtsev-Petviashvili (D$\Delta$mKP) hierarchy converts the D$\Delta$mKP system to the relativistic Toda spectra
Externí odkaz:
http://arxiv.org/abs/2304.14691
In this paper we aim to derive solutions for the SU($\mathcal{N}$) self-dual Yang-Mills (SDYM) equation with arbitrary $\mathcal{N}$. A set of noncommutative relations are introduced to construct a matrix equation that can be reduced to the SDYM equa
Externí odkaz:
http://arxiv.org/abs/2211.08574
Publikováno v:
Open Communications in Nonlinear Mathematical Physics, Volume 3 (February 6, 2023) ocnmp:10036
In this paper we develop a bilinearisation-reduction approach to derive solutions to the classical and nonlocal nonlinear Schr\"{o}dinger (NLS) equations with nonzero backgrounds. We start from the second order Ablowitz-Kaup-Newell-Segur coupled equa
Externí odkaz:
http://arxiv.org/abs/2209.04826
Autor:
Li, Shangshuai, Zhang, Da-jun
Publikováno v:
In Journal of Geometry and Physics January 2025 207
Publikováno v:
In Applied Mathematics Letters January 2025 159