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Deep learning neural networks for the third-order nonlinear Schrodinger equation: bright solitons, breathers, and rogue waves

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Communications in Theoretical Physics 2021年第10期73卷 55-63页

作者： Zijian Zhou zhenya yan Key Laboratory of Mathematics Mechanization Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

The dimensionless third-order nonlinear Schrodinger equation(alias the Hirota equation) is investigated via deep leaning neural networks. In this paper, we use the physics-informed neural networks(PINNs) deep learning method to explore the data-driven solutions(e.g. bright soliton,breather, and rogue waves) of the Hirota equation when the two types of the unperturbated and perturbated(a 2% noise) training data are considered. Moreover, we use the PINNs deep learning to study the data-driven discovery of parameters appearing in the Hirota equation with the aid of bright solitons.

关键词： third-order nonlinear Schrodinger equation deep learning data-driven solitons data-driven parameter discovery

The Sasa-Satsuma equation with high-order discrete spectra in space-time solitonic regions:soliton resolution via the mixed■-Riemann-Hilbert problem

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Communications in Theoretical Physics 2024年第6期76卷 13-25页

作者： Minghe Zhang zhenya yan KLMM Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China

In this paper,we investigate the Cauchy problem of the Sasa-Satsuma(SS)equation with initial data belonging to the Schwartz *** SS equation is one of the integrable higher-order extensions of the nonlinear Schrödinger equation and admits a 3×3 Lax *** the aid of the■nonlinear steepest descent method of the mixed■-Riemann-Hilbert problem,we give the soliton resolution and long-time asymptotics for the Cauchy problem of the SS equation with the existence of second-order discrete spectra in the space-time solitonic regions.

关键词： Sasa-Satsuma equation inverse scattering ■-Riemann-Hilbert problem ■steepest descent method soliton resolution

Symmetry Reductions, Integrability and Solitary Wave Solutions to High-Order Modified Boussinesq Equations with Damping Term

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Communications in Theoretical Physics 2001年第7期36卷 1-6页

作者： yan zhenya XIE FuDing ZHANG HongQing Department of Applied Mathematics Dalian University of Technology Dalian 116024 China Department of Applied Mathematics Dalian University of Technology Dalian 116024 China Department of Applied Mathematics Dalian University of Technology Dalian 116024 China

Both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou are extended to reduce the high-order modified Boussinesq equation with the damping term (HMBEDT) arising in the general Fermi-Pasta-Ulam model. As a result, several types of similarity reductions are obtained. It is easy to show that the nonlinear wave equation is not integrable under the sense of AblowRz's conjecture from the reduction results obtained. In addition, kink-shaped solitary wave solutions, which are of important physical significance, are found for HMBEDT based on the obtained reduction equation.

关键词： modified Boussinesq equation with the damping term, nonlinear evolution equation, symmetry reduction, integrability, solitary wave solution

Data-driven parametric soliton-rogon state transitions for nonlinear wave equations using deep learning with Fourier neural operator

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Communications in Theoretical Physics 2023年第2期75卷 5-17页

作者： Ming Zhong zhenya yan Shou-Fu Tian KLMM Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China School of Mathematics China University of Mining and TechnologyXuzhou 221116China

In this paper,we develop the deep learning-based Fourier neural operator(FNO)approach to find parametric mappings,which are used to approximately display abundant wave structures in the nonlinear Schr?dinger(NLS)equation,Hirota equation,and NLS equation with the generalized PT-symmetric Scarf-II ***,we analyze the state transitions of different types of solitons(*** solitons,breathers,peakons,rogons,and periodic waves)appearing in these complex nonlinear wave *** checking the absolute errors between the predicted solutions and exact solutions,we can find that the FNO with the Ge Lu activation function can perform well in all cases even though these solution parameters have strong influences on the wave ***,we find that the approximation errors via the physics-informed neural networks(PINNs)are similar in magnitude to those of the ***,the FNO can learn the entire family of solutions under a given distribution every time,while the PINNs can only learn some specific solution each *** results obtained in this paper will be useful for exploring physical mechanisms of soliton excitations in nonlinear wave equations and applying the FNO in other nonlinear wave equations.

关键词： deep learning Fourier neural operator solitonrogon state transition nonlinear Schrödinger equation hirota equation

Vector semi-rational rogon-solitons and asymptotic analysis for any multi-component Hirota equations with mixed backgrounds

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Communications in Theoretical Physics 2022年第9期74卷 6-22页

作者： Weifang Weng Guoqiang Zhang Shuyan Chen Zijian Zhou zhenya yan KLMM Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100049China Institute of Applied Physics and Computational Mathematics Beijing 100088China

The Hirota equation can be used to describe the wave propagation of an ultrashort optical *** this paper,the multi-component Hirota(alias n-Hirota,i.e.n-component third-order nonlinear Schrodinger)equations with mixed non-zero and zero boundary conditions are *** employ the multiple roots of the characteristic polynomial related to the Lax pair and modified Darboux transform to find vector semi-rational rogon-soliton solutions(*** combinations of rogon and soliton solutions).The semi-rational rogon-soliton features can be modulated by the polynomial *** the larger solution parameters,the first m(m

关键词： Multi-component Hirotaequations mixedbackgrounds modified Darbouxtransform semi-rational RWs and W-shaped solitons asymptotic analysis

A NEW HIERARCHY OF LAX AND LIOUVILLE INTEGRABLE EVOLUTION EQUATIONS ASSOCIATED WITH AN ISOSPECTRAL PROBLEM IN THE LOOP ALGEBRA■

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Journal of Systems Science & Complexity 2006年第3期19卷 301-306页

作者： zhenya yan Key Laboratory of Mathematics Mechanization Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China.

In this paper, an isospectral problem with five potentials is investigated in loop algebra A2 such that a new hierarchy of evolution equations with five arbitrary functions is obtained. And then by fixing the five arbitrary functions to be certain flmctions and using the trace identity, the generalized Hamiltonian structure of the hierarchy of evolution equations is given, it is shown that this hierarchy of equations is Liouville integrable. Finally some special cases of the isospectral problem are also given.

关键词： Isospectral problem loop algebra Lax integrable Liouville integrable Hamiltonian structure.

Deep learning neural networks for the third-order nonlinear Schr?dinger equation: bright solitons, breathers, and rogue waves

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Communications in Theoretical Physics 2021年第10期73卷 57-65页

作者： Zijian Zhou zhenya yan Key Laboratory of Mathematics Mechanization Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Mathematical Sciences University of Chinese Academy of Sciences

The dimensionless third-order nonlinear Schr?dinger equation(alias the Hirota equation) is investigated via deep leaning neural networks. In this paper, we use the physics-informed neural networks(PINNs) deep learning method to explore the data-driven solutions(e.g. bright soliton,breather, and rogue waves) of the Hirota equation when the two types of the unperturbated and perturbated(a 2% noise) training data are considered. Moreover, we use the PINNs deep learning to study the data-driven discovery of parameters appearing in the Hirota equation with the aid of bright solitons.

关键词：

BLIND CHANNEL AND SYMBOL JOINT ESTIMATION IN COOPERATIVE MIMO FOR WIRELESS SENSOR NETWORK

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Journal of Electronics(China) 2008年第4期25卷 439-444页

作者： yan zhenya Zheng Baoyu Institute of Signal Processing ＆ Transmission Nanjing University of Posts and Telecommunications Nanjing 210003 China

In this paper,application of Sequential Quasi Monte Carlo(SQMC)to blind channel andsymbol joint estimation in cooperative Multiple-Input Multiple-Output(MIMO)system is proposed,which does not need to transmit training symbol and can save the power and channel ***,an improved version of SQMC algorithm by taking advantage of current received signal *** results show that the SQMC method outperforms the Sequential Monte Carlo(SMC)methods,and the incorporation of current received signal improves the performance of theSQMC obviously.

关键词： Cooperative Multiple-Input Multiple-Output (MIMO) Sensor network Sequential Quasi Monte Carlo (SQMC)

Bcklund transformation, non-local symmetry and exact solutions for (2+1)-dimensional variable coefficient generalized KP equations

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Communications in Nonlinear Science and Numerical Simulation 2000年第1期5卷 31-35页

作者： zhenya yan Institute of Mathematical Science, Dalian University of Technology, Dalian 116024, China e-mail: zhanghq@dlut. *** Institute of Mathematical Science Dalian University of Technology Dalian 116024 China

With the aid of MATHEMATICA, the idea of improved homogeneous balance method is extended to (2+1)-dimensional variable coefficients KP equation. As a result, Backlund transformation and non-local symmetry are found. Then via using the Backlund transformation, six families of exact solutions for (2+1)-dimensional variable coefficients KP equation are obtained, which contain new soliton-like solutions.

关键词： variable coefficient generalized KP equation Backlund transformation nonlocal symmetry exact solution soliton