On the uniqueness of traveling waves in perturbed Korteweg-de Vries equations

DOI10.1007/BF03167282zbMath0806.35154MaRDI QIDQ1328987

Gianne Derks, Stephan A. van Gils

Publication date: 29 June 1994

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

elliptic integralsunique bifurcation point of traveling wave solutions

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Bifurcations in context of PDEs (35B32)

Related Items (20)

Existence of kink waves and periodic waves for a perturbed defocusing mKdV equation ⋮ The solitary wave, kink and anti-kink solutions coexist at the same speed in a perturbed nonlinear Schrödinger equation ⋮ Existence of solitary waves and periodic waves for a perturbed generalized BBM equation ⋮ The dynamic properties of a generalized Kawahara equation with Kuramoto-Sivashinsky perturbation ⋮ Existence of periodic waves for a perturbed quintic BBM equation ⋮ Solitary waves of singularly perturbed generalized KdV equation with high order nonlinearity ⋮ Traveling waves in a quintic BBM equation under both distributed delay and weak backward diffusion ⋮ Traveling waves of delayed Zakharov-Kuznetsov Kuramoto-Sivashinsky equation ⋮ Existence of traveling wave solutions for the perturbed modefied Gardner equation ⋮ Limit speed of traveling wave solutions for the perturbed generalized KdV equation ⋮ Existence of traveling waves in a delayed convecting shallow water fluid model ⋮ Two-dimensional patterns of pulses appearing in a thin viscous film flow ⋮ Time behaviour of the error when simulating finite-band periodic waves. The case of the KdV equation ⋮ Periodic traveling waves in a generalized BBM equation with weak backward diffusion and dissipation terms ⋮ Periodic travelling waves and their modulation ⋮ Dynamics of traveling waves for the perturbed generalized KdV equation ⋮ Coexistence of the solitary and periodic waves in convecting shallow water fluid ⋮ New solitary wave solutions in a perturbed generalized BBM equation ⋮ A New Type of Solitary Wave Solution of the mKdV Equation Under Singular Perturbations ⋮ Persistence of solitary wave solutions to a singularly perturbed generalized mKdV equation

Uses Software

• Maple

Cites Work

• Abelian integrals and bifurcation theory
• Applications of centre manifold theory
• A short proof of the inclusion of the core in the Weber set
• Attractors and transients for a perturbed periodic KdV equation: A nonlinear spectral analysis
• Stability and instability of solitary waves of Korteweg-de Vries type
• The Korteweg-de Vries equation: a historical essay
• On the stability of KdV multi‐solitons
• Unnamed Item

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