The Modulated Phase Shift for Weakly Dissipated Nonlinear Oscillatory Waves of the Korteweg-deVries Type

DOI10.1002/sapm198878173zbMath0647.35079OpenAlexW2270049962MaRDI QIDQ3791593

Richard Haberman

Publication date: 1988

Published in: Studies in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/sapm198878173

zbMATH Keywords

linearizationdispersion relationphase shiftKdV type equationsslowly varying coefficientsoscillatory wavesperturbation of the wave numberwave action equations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (13)

Whitham systems and deformations ⋮ Slowly Varying Solitary Wave Solutions of the Perturbed Korteweg‐de Vries Equation Revisited ⋮ The slowly varying phase shift for perturbed, single and multi-phased, strongly nonlinear, dispersive waves ⋮ Variation of wave action: Modulations of the phase shift for strongly nonlinear dispersive waves with weak dissipation ⋮ Multi-phase solutions of the Benjamin-Ono equation and their averaging ⋮ The multi-dimensional Hamiltonian structures in the Whitham method ⋮ Whitham equations and phase shifts for the Korteweg–de Vries equation ⋮ On the minimal set of conservation laws and the Hamiltonian structure of the Whitham equations ⋮ Phase Shift Modulations for Stable, Oscillatory, Traveling, Strongly Nonlinear Waves ⋮ The Lorentz-invariant deformation of the Whitham system for the nonlinear Klein-Gordon equation ⋮ On the canonical forms of the multi-dimensional averaged Poisson brackets ⋮ Long wave interaction over varying topography ⋮ Modulation solutions for the Benjamin-Ono equation

Cites Work

• Asymptotic solutions of nonlinear second order differential equations with variable coefficients
• A perturbation method for nonlinear dispersive wave problems
• Unnamed Item

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