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Mathematics & Statistics

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**Speaker**

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D-bar method and its application to nonlinear evolution equations

Fudong Wang

2:00pm–3:00pm

CMC 108

**Abstract**

Starting with a spectral problem, we will discuss how to generate some famous nonlinear evolution equations, such as NLS, mKdV, and DNLS. An example of how to derive pure (multi-)soliton solutions for DNLS will be presented, based on Jyh-Hao Lee's work on the global solvability of the DNLS (1989).

**Title**

**Speaker**

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Multiple component mKdV systems and their classical reductions

Alle Adjiri

2:00pm–3:00pm

PED 110

**Abstract**

In this presentation, I am going to talk about classical reductions of multiple component mKdV systems, and discuss about soliton solutions to the reduced systems, based on Riemannn-Hilbert problems.

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**Speaker**

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Nonlocal PT-symmetric integrable equations and their Riemann-Hilbert problems, II

Wen-Xiu Ma

2:00pm–3:00pm

CMC 108

**Title**

**Speaker**

**Time**

**Place**

Nonlocal PT-symmetric integrable equations and their Riemann-Hilbert problems

Wen-Xiu Ma

2:00pm–3:00pm

PED 110

**Abstract**

The talk aims to discuss how to construct nonlocal PT-symmetric integrable equations from nonlocal group reductions of matrix spectral problems. Such nonlocal equations can be classified into three types: reserve space, reverse time, and reverse spacetime, each of which can involve either the transpose or the Hermitian transpose. Notably there exist only five nonlocal PT-symmetric nonlinear Schrödinger and modified Korteweg-de Vires equations. Based on their associated spectral problems, a kind of Riemann-Hilbert problems is formulated and used to present the corresponding inverse scattering transforms. Soliton solutions are generated from solutions to special Riemann-Hilbert problems with the identity jump matrix.

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**Speaker**

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Characteristic set method combined with Lie symmetry method for differential-difference systems

Wenting Li

Heilongjiang University

China

2:00pm–3:00pm

CMC 108

**Abstract**

This talk will give an introduction to the characteristic set method, focusing on the basic idea and combination with Lie symmetry method. An application to the Toda lattice equation will be given to show how the combined algorithm works.

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**Speaker**

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Hirita bilinear forms for some nonlinear Schrödinger equations, II

Yan Jiang

Beijing University of Posts and Telecommunications

China

2:00pm–3:00pm

CMC 108

**Title**

**Speaker**

**Time**

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Hirita bilinear forms for some nonlinear Schrödinger equations

Yan Jiang

Beijing University of Posts and Telecommunications

China

2:00pm–3:00pm

PED 110

**Abstract**

In this talk, I will first review some basic concepts of the bilinear method. Then, with the bilinear mehtod, I will discuss how to obtain Hirota bilinear forms and soliton solutions for some nonlinear Schrödinger (NLS) equations, including the standard NLS equation, the derivative NLS equation and the Sasa–Satsuma equation. Note that we need to make use of some extra formulas and introduce an auxiliary function for some NLS equations. Our discussions might be helpful for obtaining Hirota bilinear forms for other nonlinear evolution equations.

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**Speaker**

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**Place**

Riemann-Hilbert approach to a coupled nonisospectral Gross-Pitaevskii system and its multi-component generalization, II

Xiaotong Chen

Zhejiang Normal University

2:00pm–3:00pm

CMC 108

**Title**

**Speaker**

**Time**

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Riemann-Hilbert approach to a coupled nonisospectral Gross-Pitaevskii system and its multi-component generalization

Xiaotong Chen

Zhejiang Normal University

2:00pm–3:00pm

PED 110

**Abstract**

In this talk, I focus on \(N\)-soliton solutions to a coupled nonisospectral Gross-Pitaevskii system by the Riemann-Hilbert approach. From the spectral problem of its Lax pair, a kind of Riemann-Hilbert problems is derived for the system, and its \(N\)-soliton solutions are then presented in the irregularity and reflectionless case. Moreover, a multi-component coupled nonisospectral Gross-Pitaevskii system will also be presented.

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**Speaker**

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Inverse scattering for nonlocal nonlinear Schrödinger hierarchies, II

Wen-Xiu Ma

2:00pm–3:00pm

CMC 108

**Title**

**Speaker**

**Time**

**Place**

Inverse scattering for nonlocal nonlinear Schrödinger hierarchies

Wen-Xiu Ma

2:00pm–3:00pm

PED 110

**Abstract**

The talk aims to discuss nonlocal nonlinear Schrödinger hierarchies and their inverse scattering transforms. The inverse scattering problems are formulated through Riemann-Hilbert problems and the closed systems for the Jost solutions are determined by the generalized Cauchy integral formula or the Sokhotski-Plemelj formula. The reflectionless transformations generate soliton solutions. A few illustrative examples will be presented.

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Damping and inhomogeneous exchange effects in the propagation of short waves in ferrites, II

Xin-wei Jin

Zhejiang Normal University

2:00pm–3:00pm

CMC 108

**Abstract**

TBA

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Damping and inhomogeneous exchange effects in the propagation of short waves in ferrites

Xin-wei Jin

Zhejiang Normal University

2:00pm–3:00pm

PED 110

**Abstract**

The Kraenkel–Manna–Merle (KMM) system is derived from the Maxwell's equations and Landau–Lifshitz–Gilbert equation to describe the propagation of short-waves in saturated ferromagnetic materials in an external field. By applying the consistent tanh expansion method and the truncated Painlevé analysis, new exact solutions including rogue waves to the KMM system are constructed, and numerical simulation is conducted to discuss the influence of damping and inhomogeneous exchange effects which exist in real circumstances.

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Rogue wave solutions to the nonlocal nonlinear Schrödinger equation, II

Rusuo Ye

Zhejiang Normal University

2:00pm–3:00pm

CMC 108

**Title**

**Speaker**

**Time**

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Rogue wave solutions to the nonlocal nonlinear Schrödinger equation

Rusuo Ye

Zhejiang Normal University

2:00pm–3:00pm

PED 110

**Abstract**

By using a matrix version of Darboux transformation with a spectral matrix of the Jordan block form, rogue wave solutions to the nonlocal nonlinear Schrödinger (NLS) equation are presented. General rogue wave solutions up to the fourth-order are also formulated. The structure of these solutions is essentially determined by the corresponding solutions of the Lyapunov equation. With appropriate choices of free parameters, dynamics and distribution patterns for the nonlocal NLS equation are shown to be much abundant than those for the local NLS equation.

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General \(N\)-solitons to nonlocal nonlinear Schrödinger equations by Riemann-Hilbert problems, II

Ahmed Ahmed

2:00pm-3:00pm

CMC 108

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**Speaker**

**Time**

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General \(N\)-solitons to nonlocal nonlinear Schrödinger equations by Riemann-Hilbert problems

Ahmed Ahmed

2:00pm–3:00pm

PED 110

**Abstract**

General \(N\)-solitons to three nonlocal nonlinear Schrödinger equations are derived from Riemann-Hilbert problems of the AKNS hierarchy. The three nonlocal equations correspond to reverse-space, reverse-time and reverse-space-time symmetries, respectively. Their \(N\)-solitons are associated with the same Riemann-Hilbert problems, but their symmetry relations of scattering data are different.

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**Speaker**

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Inverse scattering and \(N\)-soliton solution for the nonlocal nonlinear Schrödinger equation

Fudong Wang

2:00pm–3:00pm

CMC 108

**Abstract**

We will discuss the inverse scattering for the nonlocal nonlinear Schrödinger equation from a special reduction of the AKNS/ZS system. Analyticity of the Jost eigenfunctions, as well as the scattering data, will be discussed in detail. The inverse scattering will finally be transferred to an oscillatory Riemann-Hilbert problem. Assuming that the initial data is reflectionless, a general \(N\)-soliton solution will be presented.

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**Speaker**

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Soliton solutions to the nonlocal nonlinear Schrödinger equation, II

Alle Adjiri

1:30pm–2:30pm

PED 105

**Title**

**Speaker**

**Time**

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Soliton solutions to the nonlocal nonlinear Schrödinger equation

Alle Adjiri

1:30pm–2:30pm

CMC 108

**Abstract**

In this seminar, I am going to discuss soliton solutions to the nonlocal nonlinear Schrödinger equation, based on the inverse scattering transform.

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Inverse scattering transform for the nonlocal NLS equation, Part II

Yeuhui Huang

North China Electric Power University

China

1:30pm–2:30pm

CMC 209

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**Speaker**

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Inverse scattering transform for the nonlocal NLS equation

Yeuhui Huang

North China Electric Power University

China

1:30pm–2:30pm

CMC 209

**Abstract**

In this seminar, we will discuss about the inverse scattering transform for the nonlocal nonlinear Schrödinger equation, and present its applications to soliton solutions.