Stationary solitons and stabilization of the collapse described by KdV-type equations with high nonlinearities and dispersion
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Publication:1965537
DOI10.1016/0375-9601(95)00173-ZzbMath1020.35521OpenAlexW2020933594MaRDI QIDQ1965537
Jean-Marc Vanden-Broeck, V. I. Karpman
Publication date: 8 February 2000
Published in: Physics Letters. A (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0375-9601(95)00173-z
KdV equations (Korteweg-de Vries equations) (35Q53) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99)
Related Items (9)
Well-posedness and ill-posedness for linear fifth-order dispersive equations in the presence of backwards diffusion ⋮ Crank-Nicolson - differential quadrature algorithms for the Kawahara equation ⋮ Soliton ensembles and solitonic structures ⋮ Exact travelling kink-like wave solutions to some nonlinear equations ⋮ Stabilization of soliton instabilities by higher order dispersion: KdV-type equations. ⋮ Lyapunov approach to the soliton stability in highly dispersive systems. II: KdV-type equations ⋮ Stationary solitons of the fifth order KdV-type. Equations and their stabilization. ⋮ An efficient approximation to numerical solutions for the Kawahara equation via modified cubic B-spline differential quadrature method ⋮ Stability of solitons described by KdV-type equations with higher-order dispersion and nonlinearity (analytical results)
Cites Work
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- Structural stability of the Korteweg-de Vries solitons under a singular perturbation
- Radiating solitons of the fifth order KdV-type equations
- Stationary solitary waves of the fifth order KdV-type equations
- Solitary and periodic gravity—capillary waves of finite amplitude
- Blow-up in Nonlinear Schroedinger Equations-I A General Review
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