Time: May 19-21, 2023

Venue: Meeting room No. 1 (BTG Fragrant Hill Hotel, Haidian district, Beijing)

May 19: Registration

May 20:

 

May 21:

 

Title: Fokas-Lenells equation on the line: Global well-posedness with solitons

Engui Fan (Fudan Univ.)

Abstract: We prove the existence of global solutions in  to the Fokas-Lenells (FL) equation on the line as the initial data includes solitons. A key tool in proving this result is a newly modified Darboux transformation, which adds or subtracts a soliton with given spectral and scattering parameters. In this way the inverse scattering transform is then applied to establish the global well-posedness of initial value problem with a finite number of solitons based on our previous results on the global well-posedness of the FL equation.

 

Title: Long-time asymptotics of mCH equation in solitonic regions

Engui Fan (Fudan Univ.)

Abstrct: We study the long time asymptotic behavior for the Cauchy problem of the modified Camassa-Holm (mCH) equation in the solitonic regions. Our main technical tool is the representation of the Cauchy problem with an associated matrix Riemann-Hilbert (RH) problem and the consequent asymptotic analysis of this RH problem by using Dbar generalization of Deift-Zhou steepest descent method.

 

Title: Complex dynamics on the one-dimensional quantum droplets via time piecewise PINNs

Yong Chen (East China Normal Univ.)

Abstract：In this talk, we propose a novel time piecewise physics-informed neural networks (PINNs) to study complex dynamics on the one-dimensional quantum droplets by solving the corresponding amended Gross-Pitaevskii equation. The training effect of this network model in the long time domain is far better than that of the conventional PINNs, and each of its subnetworks is independent and highly adjustable. By using time piecewise PINNs with scarce training points, we not only study intrinsic modulation of single droplet and collision between two droplets, but also excite the breathers on droplet background.

 

Title: Computer and Nonlinear Sciences-integrable deep learning

Yong Chen (East China Normal Univ.)

Abstract: From the relationship between computer and nonlinear scientific research-FPU problem to soliton theory, which triggered my thinking on the research of integrable systems-propose an integrable deep learning framework. Introduce our related work and latest developments in integrable deep learning

 

Title: Mix-training physics-informed neural networks for the rogue waves of nonlinear Schrodinger equation

Biao Li (Ningbo Univ.)

Abstract：In this talk, we propose Mix-training physics-informed neural networks (PINNs), a deep learning model with more approximation ability based on PINNs, combined with mixed training and prior information. We demonstrate the advantages of this model by exploring rogue waves with rich dynamic behavior in the nonlinear Schrodinger (NLS) equation. Numerical results show that compared with the original PINNs, this model can not only quickly recover the dynamical behavior of the rogue waves of NLS equation, but also significantly improve its approximation ability and absolute error accuracy, the prediction accuracy improved by two to three orders of magnitude.

 

Title: Higher-order smooth positons and breather positons of nonlinear wave equations

Biao Li (Ningbo Univ.)

Abstract: Based on the Hirota bilinear method, a more classic limit technique is perfected to obtain second-order

smooth positons. Immediately afterwards, we propose an extremely ingenious limit approach in which higher- order smooth positons and breather positons can be quickly derived from N-soliton solution. Under this ingenious technique, the smooth positons and breather positons of the modified KdV system are quickly and easily derived.

 

Title: Singular-loop rogue wave and mixed interaction solutions with location control parameters for WKI equation

Xiaoyong Wen (Beijing Infor. Sci. Tech. Univ.)

Abstract：In this work, we study the complete integrable Wadati–Konno–Ichikawa equation with important physical background. Based on the known hodograph transformation, we give an alternative two-component nonlinear system of this equation. By constructing its special generalized (m, N？m)-fold Darboux transformation, we obtain various location-manageable localized wave solutions, like higher-order rogue wave and periodic wave solutions with smooth, singular and singular-loop structures. It is found that the rogue wave can show a singular-loop structure if the special parameters are selected. For the first-order exact solutions, we analyze and summarize the reasons for singular structures when the plane wave amplitude reaches a certain value. Furthermore, we also discuss and summarize mixed interaction structures of diverse localized waves. .

 

Title: Integrable Ermakov structure、Lax pari and vortex solutions in compressible NS equation

Hongli An (Nanjing Agricultural Univ.)

Abstract: In this talk, we investigate the 2+1-dimensional compressible NS equation with density-dependent viscosity coefficients. We introduce a novel power-type elliptic vortex ansatz and thereby obtain a finite-dimensional nonlinear dynamical system. The latter is shown to not only have an underlying integrable Ermakov structure of Hamiltonian type, but also admit a Lax pair formulation and associated stationary NLS connection. In addition, we construct a class of elliptical vortex solutions termed pulsrodons corresponding to pulsating elliptic warm core eddies and discuss their dynamical behaviors.

 

Title: Dynamical analysis of mixed burster and their transitions

Zhuosheng Lü ( Beijing Univ. Posts and Telecommunications)

Abstract: In this talk, we explain how the generation and transition of mixed burster effected by intrinsic parameter and current stimulation. We show several special mixed bursters one after another and interpret their dynamical mechanisms via fast–slow decomposition and two-parameter bifurcation analysis.

 

Title: Nonlocal residual symmetry and soliton-elliptic periodic wave interaction solutions for the variable coefficient coupled Lakshmanan-Porsezian-Daniel equations 

Xueping Cheng (Zhejiang Ocean Univ.)              

Abstract：In this talk, the nonlocal residual symmetry for the complex functional integrable equation, i.e. coupled LPD equations with time varying coefficients, is first studied from the truncated Painleve expansion, After localizing the nonlocal symmetry into the local Lie point symmetry, the group invariant solutions have been constructed via the classical symmetry reduction technique. The explicit soliton-elliptic periodic wave interaction solutions for variable coefficient coupled LPD equations are derived. The controllable evolution behaviors of the interaction solutions are displayed in graphical way by fixing the variable wave parameters at certain values.

 

Title: Pseudopotentials and Nonlinear Waves

Yunqing Yang (Zhejiang Univ. Science & Technology)

Abstract: In this talk, we first introduce the pseudopotentials of integrable systems, from which some integrable properties and Darboux transformations are derived. Secondly, the concepts of pseudopotentials are generalized to the nonlocal and discrete integrable systems, form which various types of nonlinear localized wave solutions on constant background and their corresponding dynamical properties are investigated. Finally, nonlinear wave solutions on constant background are generalized to the nonconstant background, and some interesting nonlinear wave solutions including soliton, breather and rogue wave solutions on two types of periodic backgrounds are constructed, and the corresponding dynamics are studied.