Whitham modulation theory for the Kadomtsev– Petviashvili equation
From MaRDI portal
Publication:4644825
DOI10.1098/rspa.2016.0695zbMath1404.35382arXiv1610.03478OpenAlexW2530467204WikidataQ52383918 ScholiaQ52383918MaRDI QIDQ4644825
Mark J. Ablowitz, Gino Biondini, Qiao Wang
Publication date: 9 January 2019
Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1610.03478
water wavesWhitham equationsKadomtsev-Petviashvili equationsmall dispersion limitdispersive shock wavesdispersive regularizations
Related Items
On the Periodic Solutions of the Davey-Stewartson Systems ⋮ Numerical study of the Kadomtsev–Petviashvili equation and dispersive shock waves ⋮ Formation of the undular bores in shallow water generalized Kaup-Boussinesq model ⋮ Whitham modulation theory for (2 + 1)-dimensional equations of Kadomtsev–Petviashvili type ⋮ Exotic wave patterns in Riemann problem of the high‐order Jaulent–Miodek equation: Whitham modulation theory ⋮ Undular bores in the \((3+1)\) dimensional mKP equation ⋮ On the Whitham system for the (2+1)‐dimensional nonlinear Schrödinger equation ⋮ Two-dimensional reductions of the Whitham modulation system for the Kadomtsev–Petviashvili equation ⋮ Evolution of truncated and bent gravity wave solitons: the Mach expansion problem ⋮ Initial-boundary value problem for stimulated Raman scattering model: solvability of Whitham type system of equations arising in long-time asymptotic analysis ⋮ Evolution of initial discontinuity for the defocusing complex modified KdV equation ⋮ Oblique interactions between solitons and mean flows in the Kadomtsev–Petviashvili equation ⋮ Integrability, exact reductions and special solutions of the KP–Whitham equations ⋮ Whitham modulation theory for the defocusing nonlinear Schrödinger equation in two and three spatial dimensions
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Wave breaking in solutions of the dispersionless Kadomtsev-Petviashvili equation at a finite time
- Computing spectra of linear operators using the Floquet-Fourier-Hill method
- Inverse scattering problem for vector fields and the Cauchy problem for the heavenly equation
- On the stability of nonlinear waves in integrable models
- A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I
- Method of averaging for two-dimensional integrable equations
- On the integrability of \((2+1)\)-dimensional quasilinear systems
- Dispersive hydrodynamics: Preface
- Dispersive shock waves and modulation theory
- Dispersive shock waves in the Kadomtsev-Petviashvili and two dimensional Benjamin-Ono equations
- Whitham theory for perturbed Korteweg-de Vries equation
- Whitham modulation equations, coalescing characteristics, and dispersive Boussinesq dynamics
- Small dispersion limit of the Korteweg-de Vries equation with periodic initial conditions and analytical description of the Zabusky-Kruskal experiment
- Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert problem approach
- The propagation of internal undular bores over variable topography
- Dispersive shock waves in nematic liquid crystals
- Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation
- Shock formation in the dispersionless Kadomtsev–Petviashvili equation
- Transverse Spectral Stability of Small Periodic Traveling Waves for the KP Equation
- Solvable vector nonlinear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking
- On the dispersionless Kadomtsev–Petviashvili equation inn+1 dimensions: exact solutions, the Cauchy problem for small initial data and wave breaking
- Soliton solutions of the Kadomtsev-Petviashvili II equation
- Scattering transform for nonstationary Schrödinger equation with bidimensionally perturbed N-soliton potential
- Spectral theory of two-dimensional periodic operators and its applications
- The Haantjes tensor and double waves for multi-dimensional systems of hydrodynamic type: a necessary condition for integrability
- Two-dimensional lumps in nonlinear dispersive systems
- On a family of solutions of the Kadomtsev–Petviashvili equation which also satisfy the Toda lattice hierarchy
- The Korteweg-de Vries, Kadomtsev-Petviashvili and Boussinesq equations. Modulation theory
- The Cauchy Problem for the Kadomtsev–Petviashili II Equation with Nondecaying Data along a Line
- Inverse scattering theory of the heat equation for a perturbed one-soliton potential
- KP solitons, total positivity, and cluster algebras
- Transverse instability for periodic waves of KP-I and Schroedinger equations
- Non-linear dispersive waves
- On the solutions of the dKP equation: the nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking
- A perturbation method for nonlinear dispersive wave problems
- Generation of undular bores in the shelves of slowly-varying solitary waves
