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Riemann–Hilbert Problems and Soliton Solutions of Type (${\lambda}^{\ast}$ , $-{\lambda}^{\ast}$ ) Reduced Nonlocal Integrable mKdV Hierarchies

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## Abstract

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## 1. Introduction

## 2. Reduced Nonlocal Matrix Integrable mKdV Hierarchies

#### 2.1. The Matrix AKNS Integrable Hierarchies Revisited

#### 2.2. Reduced Nonlocal Matrix Integrable mKdV Hierarchies

## 3. Riemann–Hilbert Problems

#### 3.1. Properties of Eigenvalues and Eigenfunctions

#### 3.2. Riemann–Hilbert Problems

#### 3.3. Evolution of the Scattering Data

#### 3.4. Gelfand–Levitan–Marchenko Type Equations

#### 3.5. Recovering the Potential Matrix

## 4. Soliton Solutions

#### 4.1. General Formulation

#### 4.2. Realization

## 5. Concluding Remarks

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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Ma, W.-X.
Riemann–Hilbert Problems and Soliton Solutions of Type (*Mathematics* **2022**, *10*, 870.
https://doi.org/10.3390/math10060870

**AMA Style**

Ma W-X.
Riemann–Hilbert Problems and Soliton Solutions of Type (*Mathematics*. 2022; 10(6):870.
https://doi.org/10.3390/math10060870

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Ma, Wen-Xiu.
2022. "Riemann–Hilbert Problems and Soliton Solutions of Type (*Mathematics* 10, no. 6: 870.
https://doi.org/10.3390/math10060870