Evolution of initial discontinuities in a particular case of two-step initial problem for the defocusing complex modified KdV equation
DOI10.1016/j.jmaa.2024.128227OpenAlexW4391925945MaRDI QIDQ6126764
Unnamed Author, Ao Zhou, Yu-Shan Xue
Publication date: 10 April 2024
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jmaa.2024.128227
PDEs in connection with fluid mechanics (35Q35) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Periodic solutions to PDEs (35B10) Shock waves and blast waves in fluid mechanics (76L05) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Analyticity in context of PDEs (35A20) NLS equations (nonlinear Schrödinger equations) (35Q55) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Bifurcations in context of PDEs (35B32) Self-similar solutions to PDEs (35C06)
Cites Work
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- Self-similar solutions of the non-strictly hyperbolic Whitham equations for the KdV hierarchy
- Decay of an initial discontinuity in the defocusing NLS hydrodynamics
- Initial value problem of the Whitham equations for the Camassa-Holm equation
- Whitham equations in the AKNS scheme
- Dispersive shock waves and modulation theory
- The complete classification of solutions to the Riemann problem of the defocusing complex modified KdV equation
- Formation of the undular bores in shallow water generalized Kaup-Boussinesq model
- Evolution of initial discontinuity for the defocusing complex modified KdV equation
- Interactions of dispersive shock waves
- Evolution of initial discontinuities in the Riemann problem for the Jaulent-Miodek equation with positive dispersion
- Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory
- The small dispersion limit of the Korteweg-de Vries equation. I
- On the Whitham Equations for the Defocusing Complex Modified KdV Equation
- Wave Breaking and the Generation of Undular Bores in an Integrable Shallow Water System
- Nonlinear Filters for Efficient Shock Computation
- Multiphase averaging and the inverse spectral solution of the Korteweg—de Vries equation
- Evolution of initial discontinuities in the Riemann problem for the Kaup-Boussinesq equation with positive dispersion
- Integrable Shallow-Water Equations and Undular Bores
- Non-linear dispersive waves
- Exotic wave patterns in Riemann problem of the high‐order Jaulent–Miodek equation: Whitham modulation theory
- The ``good Boussinesq equation: long-time asymptotics
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