Shoufeng Shen

The decomposition, asymptotic behavior and hyperbolic representation of the multiloop soliton and multibreather solutions to the WKI elastic beam equation

Xiaorui Hu, Junyang Zhang, Shoufeng Shen

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Limit solutions of loop solitons for a compound WKI-SP equation

QU Gai-zhu, Junyang Zhang, Xiaorui Hu, Shoufeng Shen

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The revised Riemann–Hilbert approach to the Kaup–Newell equation with a non-vanishing boundary condition: Simple poles and higher-order poles

Yongshuai Zhang, Deqin Qiu, Shoufeng Shen, Jingsong He

With a non-vanishing boundary condition, we study the Kaup–Newell (KN) equation (or the derivative nonlinear Schrödinger equation) using the Riemann–Hilbert approach. Our study yields four types of Nth order solutions of the KN equation that corresponding to simple poles on or not …

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Cauchy matrix approach for H1 a equation in the torqued Adler–Bobenko–Suris lattice list

Jing Wang, Song‐lin Zhao, Shoufeng Shen

Abstract As a torqued version of the lattice potential Korteweg–de Vries equation, the H1 a is an integrable nonsymmetric lattice equation with only one spacing parameter. In this paper, we present the Cauchy matrix scheme for this equation. Soliton solutions, Jordan-block solutions …

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Multiloop soliton solutions and compound WKI–SP hierarchy

Xiaorui Hu, Tian‐Le Xu, Junyang Zhang, Shoufeng Shen

Abstract In this paper, a compound equation which is a mix of the Wadati–Konno–Ichikawa (WKI) equation and the short‐pulse (SP) equation is first studied. By transforming both the independent and dependent variables in the equation, we introduce a novel hodograph transformation to …

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Continuum limits for rational, breather solutions, and gauge equivalent model of the generalized discrete nonlinear Schrödinger equation

Li-Yuan Ma, Haifang Song, Yanli Zhang, Shoufeng Shen

In this paper, we focus on an integrable higher‐order discrete nonlinear Schrödinger (dNLS) equation, which yields the Lakshmanan–Porsezian–Daniel (LPD) equation in the continuum limit. The breather solutions of the higher‐order dNLS are obtained for the first time. We show that the rational …

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Solutions to Kadomtsev-Petviashvili system: generalized Cauchy matrix approach

Song‐lin Zhao, Shoufeng Shen

Generalized Cauchy matrix approach for non-autonomous discrete Kadomtsev-Petviashvili system

Song‐lin Zhao, Wei Feng, Shoufeng Shen, Jun Zhang

In this paper, we investigate the non-autonomous discrete Kadomtsev-Petviashvili (KP) system in terms of generalized Cauchy matrix approach. These equations include non-autonomous bilinear lattice KP equation, non-autonomous lattice potential KP equation, non-autonomous lattice potential modified KP equation, non-autonomous asymmetric lattice potential modified …

Kadomtsev-Petviashvili system and reduction: generalized Cauchy matrix approach

Song‐lin Zhao, Shoufeng Shen, Wei Feng

By the Sylvester equation $\bL\bM-\bM\bK=\br\bs^{\st}$ together with an evolution equation set of $\br$ and $\bs$, generalized Cauchy matrix approach is established to investigate exact solutions for Kadomtsev-Petviashvili system, including Kadomtsev-Petviashvili equation, modified Kadomtsev-Petviashvili equation and Schwarzian Kadomtsev-Petviashvili equation. The matrix $\bM$ provides …