Stability of cnoidal waves
By Jaime Angulo Pava, Jerry L. Bona, M. Scialom. Advances in Differential Equations, 2006
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This paper is concerned with the stability of periodic trave- lling-wave solutions of the Korteweg-de Vries equation ut + uux + uxxx =0 . Here, u is a real-valued function of the two variables x, t ∈ R and subscripts connote partial differentiation. These special solutions were termed cnoidal waves by Korteweg and de Vries. They also appear in earlier work of Boussinesq. It is shown that these solutions are stable to small, periodic perturbations in the context of the initial-value problem. The approach is that of the modern theory of stability of solitary waves, but adapted to the periodic context. The theory has prospects for the study of periodic travelling-wave solutions of other partial differential equations.
Subfields: Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/d10969d8c399cb3bd1fb787a25d7925c399105d4
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Citations in the corpus
- An Instability Index Theory for Quadratic Pencils and Applications (2012, background): “M1(a;E;c;b);Pe(a;E;c;b);M2(a;E;c;b) 2R4 is a local diffeomorphism from a neighborhood of (a0;E0;c0;b0) onto a neighborhood of the point (T;M1;eP;M 2)(a0;E0;c0;b0): It follows that we can find a curve [0;1] 3s7!(a(s);E(s);c(s);b(s)) 2R4 with (a(0);E(0);c(0);b(0)) = (0;0;0;0) such that for each s2[0;1]”
- Instability, index theorem, and exponential trichotomy for Linear Hamiltonian PDEs (2017, unknown): “[2] [3] [41] [34] [11] [8]) by using Liapunov functionals.”