Undular bores and the initial-boundary value problem for the modified Korteweg-de Vries equation

DOI10.1016/j.wavemoti.2007.11.003zbMath1231.35208OpenAlexW2046369125MaRDI QIDQ661629

Juan-Miguel Gracia

Publication date: 11 February 2012

Published in: Wave Motion (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.wavemoti.2007.11.003

zbMATH Keywords

initial-boundary value problemsolitonundular boremodified Korteweg-de Vries equationmodulation theory

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Solitary waves for incompressible inviscid fluids (76B25) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40)

Related Items (13)

Whitham modulation theory for (2  +  1)-dimensional equations of Kadomtsev–Petviashvili type ⋮ The large-time asymptotic solution of the mKdV equation ⋮ Undular bores in the \((3+1)\) dimensional mKP equation ⋮ Dispersive and Diffusive-Dispersive Shock Waves for Nonconvex Conservation Laws ⋮ Solitary-wave solutions of Benjamin-Ono and other systems for internal waves. II: Dynamics ⋮ On the Long-Time Asymptotic Behavior of the Modified Korteweg--de Vries Equation with Step-like Initial Data ⋮ Emergence of Solitonic Structures in Hierarchical Korteweg–de Vries Systems ⋮ Dispersive shock waves in systems with nonlocal dispersion of Benjamin–Ono type ⋮ Dynamic soliton–mean flow interaction with non-convex flux ⋮ Dispersive shock waves and modulation theory ⋮ Laguerre polynomials and transitional asymptotics of the modified Korteweg-de Vries equation for step-like initial data ⋮ Genuine nonlinearity and its connection to the modified Korteweg–de Vries equation in phase dynamics ⋮ Travelling wave solutions on a non-zero background for the generalized Korteweg–de Vries equation

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