The Well and Box Types Initial Value Problems of the Defocusing mKdV Equation
Abstract
Abstract We study the time evolution problems of special initial values with two discontinuities for the defocusing mKdV equation. Based on the finite-gap integral method, Whitham modulation system of the defocusing mKdV equation is derived in the form of Riemann invariants, and full-time evolution results for six types of initial values with two discontinuities are obtained in detail. The regions where rarefaction waves interact with dispersive shock waves are thoroughly analyzed. Two novel phenomena, namely soliton trains and linear wave packets, are identified and their intrinsic mechanisms are systematically illustrated. All the results are verified by numerical simulations.
Fields of Study & Subjects
Nonlinear Waves and Solitons
Fractional Differential Equations Solutions
Nonlinear Photonic Systems
Publication details
- Journal / source
- Chinese Physics Letters
- Publisher
- IOP Publishing
- Volume
- 43
- Issue
- 4
- Pages
- 040001–040001
- Publication date
- 27 February 2026