On the stable self-similar waves for the Camassa-Holm and Degasperis-Procesi equations
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Publication:2196582
zbMath1447.35271MaRDI QIDQ2196582
Weiping Yan, Liangchen Li, Hengyan Li
Publication date: 3 September 2020
Published in: Advances in Differential Equations (Search for Journal in Brave)
Full work available at URL: https://projecteuclid.org/euclid.ade/1589594421
PDEs in connection with fluid mechanics (35Q35) Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Singularity in context of PDEs (35A21) Self-similar solutions to PDEs (35C06)
Cites Work
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- The Degasperis-Procesi equation as a non-metric Euler equation
- On well-posedness of the Degasperis-Procesi equation
- On the well-posedness of the Degasperis-Procesi equation
- The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
- Global weak solutions and blow-up structure for the Degasperis-Procesi equation
- Global conservative solutions of the Camassa-Holm equation
- Formation and dynamics of shock waves in the Degasperis-Procesi equation
- Stability of a class of solitary waves in compressible elastic rods
- Semigroups of linear operators and applications to partial differential equations
- Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. II: The KdV-equation
- Wave breaking for nonlinear nonlocal shallow water equations
- The Hamiltonian structure of the Camassa-Holm equation
- On the Cauchy problem for the periodic Camassa-Holm equation
- On the Cauchy problem for an integrable equation with peakon solutions
- Global weak solutions for a shallow water equation
- Stability of the Camassa-Holm solitons
- Integrability of invariant metrics on the Virasoro group
- Existence of permanent and breaking waves for a shallow water equation: a geometric approach
- Asymptotic stability and instability of explicit self-similar waves for a class of nonlinear shallow water equations
- Exact solutions in invariant manifolds of some higher-order models describing nonlinear waves
- Global existence and blow-up phenomena for the Degasperis-Procesi equation
- Large time existence for 3D water waves and asymptotics
- Local-in-space criteria for blowup in shallow water and dispersive rod equations
- A generalized nonisospectral Camassa-Holm equation and its multipeakon solutions
- On permanent and breaking waves in hyperelastic rods and rings
- On the scattering problem for the Camassa-Holm equation
- Norm Inflation and Ill-Posedness for the Degasperis-Procesi Equation
- GLOBAL DISSIPATIVE SOLUTIONS OF THE CAMASSA–HOLM EQUATION
- Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
- Breakdown of the Camassa-Holm equation
- Stability of peakons
- An integrable shallow water equation with peaked solitons
- Camassa–Holm, Korteweg–de Vries and related models for water waves
- More on Bifurcations and Dynamics of Traveling Wave Solutions for a Higher-Order Shallow Water Wave Equation
- Prolongation algebras and Hamiltonian operators for peakon equations
- Local Well-Posedness and Orbital Stability of Solitary Wave Solutions for the Generalized Camassa–Holm Equation
- The role of self-similarity in singularities of partial differential equations
- Model equations for long waves in nonlinear dispersive systems
- Orbital stability of solitary waves for a shallow water equation
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