Abstract
In this paper, we systematically study the integrability and data-driven solutions of the nonlocal mKdV equation. The infinite conservation laws of the nonlocal mKdV equation and the corresponding infinite conservation quantities are given through Riccti equation. The data-driven solutions of the zero boundary for the nonlocal mKdV equation are studied by using the multilayer physical information neural network algorithm, which include kink soliton, complex soliton, bright-bright soliton and the interaction between soliton and kink-type. For the data-driven solutions with nonzero boundary, we study kink, dark, anti-dark and rational solution. By means of image simulation, the relevant dynamic behavior and error analysis of these solutions are given. In addition, we discuss the inverse problem of the integrable nonlocal mKdV equation by applying the physics-informed neural network algorithm to discover the parameters of the nonlinear terms of the equation.
| Original language | English |
|---|---|
| Pages (from-to) | 8397-8417 |
| Number of pages | 21 |
| Journal | Nonlinear Dynamics |
| Volume | 111 |
| Issue number | 9 |
| DOIs | |
| State | Published - May 2023 |
Keywords
- Conservation laws
- Inverse problem
- Kink soliton
- Nonlocal mKdV equation
- Physics-informed neural network