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Chinese Physics B 2023年第12期32卷 263-269页

作者：刘锦洲闫鑫颖金梦辛祥鹏 School of Mathematical Sciences Liaocheng UniversityLiaocheng 252059China

This article presents the construction of a nonlocal Hirota equation with variable coefficients and its Darboux *** zero-seed solutions,1-soliton and 2-soliton solutions of the equation are constructed through the Darboux transformation,along with the expression for N-soliton *** of coefficients that are taken as a function of time instead of a constant,i.e.,coefficient functionδ(t),on the solutions is investigated by choosing the coefficient functionδ(t),and the dynamics of the solutions are *** article utilizes the Lax pair to construct infinite conservation laws and extends it to nonlocal *** study of infinite conservation laws for nonlocal equations holds significant implications for the integrability of nonlocal equations.

关键词： infinite conservation laws nonlocal Hirota equation with variable coefficient soliton solutions Darboux transformation

Hamiltonian System and infinite conservation laws Associated with a New Discrete Spectral Problem

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Communications in Theoretical Physics 2008年第6期49卷 1399-1402页

作者： LUO Lin FAN En-Gui Department of Mathematics Xiaogan University Xiaogan 432100 China School of Mathematics Fudan University Shanghai 200433 China

Starting from a new discrete spectral problem, the corresponding hierarchy of nonlinear lattice equations is proposed. It is shown that the lattice soliton hierarchy possesses the bi-Hamiltonian structures and infinit... 详细信息

关键词： Hamiltonian system infinite conservation laws discrete spectral problem

Backlund transformation,infinite number of conservation laws and fission properties of an integro-differential model for ocean internal solitary waves

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Communications in Theoretical Physics 2021年第3期73卷 36-42页

作者： Di Yu Zong-Guo Zhang Huan-He Dong Hong-Wei Yang College of Mathematics and System Science Shandong University of Science and TechnologyQingdao 266590China School of Mathematics and Statistics Qilu University of Technology(Shandong Academy of Sciences)Jinan250353China

This paper presents an analytical investigation of the propagation of internal solitary waves in the ocean of finite *** the multi-scale analysis and reduced perturbation methods,the integro-differential equation is derived,which is called the intermediate long wave(ILW)equation and can describe the amplitude of internal solitary *** can reduce to the Benjamin-Ono equation in the deep-water limit,and to the KdV equation in the shallow-water *** attention has been paid to the features of integro-differential equations,especially for their conservation ***,based on Hirota bilinear method,Backlund transformations in bilinear form of ILW equation are derived and infinite number of conservation laws are ***,we analyze the fission phenomenon of internal solitary waves theoretically and verify it through numerical *** of these have potential value for the further research on ocean internal solitary waves.

关键词： infinite conservation laws the integro-differential equation internal solitary waves fission properties of waves

An extension of integrable equations related to AKNS and WKI spectral problems and their reductions

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Chinese Physics B 2018年第4期27卷 134-137页

作者： Xian-Guo Geng Yun-Yun Zhai School of Mathematics and Statistics Zhengzhou University Zhengzhou 450001 China

A novel hierarchy of integrable nonlinear evolution equations related to the combined Ablowitz–Kaup–Newell–Segur（AKNS） and Wadati–Konno–Ichikawa（WKI） spectral problems is proposed,from which the Lax pair for a corresponding negative flow and its infinite many conservation laws are ***,a reduction of this hierarchy is discussed,by which a generalized sinh-Gordon equation is derived on the basis of its negative flow.

关键词： integrable extension nonlinear evolution equations infinite conservation laws

Two integrable generalizations of WKI and FL equations: Positive and negative flows, and conservation laws

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Chinese Physics B 2020年第5期29卷 70-73页

作者： Xian-Guo Geng Fei-Ying Guo Yun-Yun Zhai School of Mathematics and Statistics Zhengzhou UniversityZhengzhou 450001China

With the aid of Lenard recursion equations, an integrable hierarchy of nonlinear evolution equations associated with a 2 × 2 matrix spectral problem is proposed, in which the first nontrivial member in the positive flows can be reduced to a new generalization of the Wadati–Konno–Ichikawa(WKI) equation. Further, a new generalization of the Fokas–Lenells(FL) equation is derived from the negative flows. Resorting to these two Lax pairs and Riccati-type equations, the infinite conservation laws of these two corresponding equations are obtained.

关键词： integrable generalizations positive flow and negative flow infinite conservation laws