The Periodic Cauchy Problem for Novikov's Equation
From MaRDI portal
Publication:3100964
DOI10.1093/imrn/rnq267zbMath1235.35011arXiv1009.1820OpenAlexW2964342860MaRDI QIDQ3100964
Publication date: 22 November 2011
Published in: International Mathematics Research Notices (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1009.1820
peakon solutionswell posednessintegrable equationperiodic initial dataCauchy-Kowalevski theoremLax pair representations
KdV equations (Korteweg-de Vries equations) (35Q53) Cauchy-Kovalevskaya theorems (35A10) Solutions to PDEs in closed form (35C05)
Related Items (72)
An Inverse Spectral Problem Related to the Geng–Xue Two-Component Peakon Equation ⋮ On the Cauchy problem and peakons of a two-component Novikov system ⋮ A Cauchy-Kovalevsky Theorem for Nonlinear and Nonlocal Equations ⋮ Some properties of solutions to the Camassa-Holm-type equation with higher-order nonlinearities ⋮ Liouville correspondences between integrable hierarchies ⋮ The power series method for nonlocal and nonlinear evolution equations ⋮ Instability and nonuniqueness for the \(b\)-Novikov equation ⋮ Ghostpeakons and characteristic curves for the Camassa-Holm, Degasperis-Procesi and Novikov equations ⋮ The existence of the single peaked traveling waves to the -Novikov equation ⋮ The Cauchy problem for a 4-parameter family of equations with peakon traveling waves ⋮ Radius of analyticity for the Camassa-Holm equation on the line ⋮ A Riemann-Hilbert approach for the Novikov equation ⋮ On the weakly dissipative Camassa-Holm, Degasperis-Procesi, and Novikov equations ⋮ The Cauchy problem for the Fokas-Olver-Rosenau-Qiao equation ⋮ On the Cauchy problem for a class of shallow water wave equations with \((k+1)\)-order nonlinearities ⋮ Non-uniform dependence on initial data for the modified \(\mu\)-Camassa-Holm equation ⋮ The initial value problem for a Novikov system ⋮ On an integrable Camassa-Holm type equation with cubic nonlinearity ⋮ Exact solitary solution and a three-level linearly implicit conservative finite difference method for the generalized Rosenau-Kawahara-RLW equation with generalized Novikov type perturbation ⋮ Persistence properties and unique continuation for a generalized Camassa-Holm equation ⋮ Construction of 2-Peakon Solutions and Ill-Posedness for the Novikov Equation ⋮ Stability of peakons for an integrable modified Camassa-Holm equation with cubic nonlinearity ⋮ The investigation of local weak solutions for a generalized Novikov equation ⋮ Local well-posedness and persistence property for the generalized Novikov equation ⋮ Well-posedness, blow-up phenomena and global existence for the generalized \(b\)-equation with higher-order nonlinearities and weak dissipation ⋮ On the Cauchy problem for the new integrable two-component Novikov equation ⋮ Stability of peakons for the Novikov equation ⋮ Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems ⋮ Local and global analyticity for theμ-Novikov equation ⋮ On a generalized Camassa‐Holm type equation with ()‐degree nonlinearities ⋮ Orbital stability of the trains of peaked solitary waves for the modified Camassa-Holm-Novikov equation ⋮ Local well-posedness and blow-up criteria for a three-component Camassa–Holm type equation ⋮ The Cauchy problem and blow-up phenomena of a new integrable two-component Camassa-Holm system ⋮ On the Cauchy problem of a new integrable two-component Novikov equation ⋮ Persistence properties and blow-up phenomena for a generalized Camassa-Holm equation ⋮ The Cauchy problem and multi-peakons for the mCH-Novikov-CH equation with quadratic and cubic nonlinearities ⋮ On the Cauchy problem for the integrable modified Camassa-Holm equation with cubic nonlinearity ⋮ Wave-breaking and peakons for a modified Camassa-Holm equation ⋮ On the Cauchy problem for the two-component Novikov equation ⋮ Curvature blow-up for the higher-order Camassa-Holm equations ⋮ The Cauchy problem on a generalized Novikov equation ⋮ Well-posedness, wave breaking and peakons for a modified \({\mu}\)-Camassa-Holm equation ⋮ Orbital stability of the train of peakons for an integrable modified Camassa-Holm equation ⋮ Global weak solutions for the two-component Novikov equation ⋮ The global solution and blow-up phenomena to a modified Novikov equation ⋮ Nonlinear perturbations of evolution systems in scales of Banach spaces ⋮ The Cauchy problem for a generalized \(b\)-equation with higher-order nonlinearities in critical Besov spaces and weighted \(L^p\) spaces ⋮ Comparison Between the Exact Solutions of Three Distinct Shallow Water Equations Using the Painlevé Approach and Its Numerical Solutions ⋮ Continuity properties of the data-to-solution map for the generalized Camassa-Holm equation ⋮ A note on the Cauchy problem of a modified Camassa-Holm equation with cubic nonlinearity ⋮ Hölder continuity for the Fokas-Olver-Rosenau-Qiao equation ⋮ The periodic boundary value problem for a quasilinear evolution equation in Besov spaces ⋮ On the optimal control problem for the Novikov equation with strong viscosity ⋮ Hölder continuity of the solution map for the Novikov equation ⋮ The Cauchy problem for a generalized Camassa-Holm equation ⋮ Global analyticity for a generalized Camassa-Holm equation and decay of the radius of spatial analyticity ⋮ A note on the generalized Camassa-Holm equation ⋮ Large time behavior of momentum support for a Novikov type equation ⋮ Well-posedness and wave breaking of the degenerate Novikov equation ⋮ Global well-posedness for the periodic Novikov equation with cubic nonlinearity ⋮ Nonuniform dependence and persistence properties for a two-component Novikov system ⋮ Unnamed Item ⋮ Analysis on the blow-up of solutions to a class of integrable peakon equations ⋮ Well-posedness and analyticity of the Cauchy problem for the multi-component Novikov equation ⋮ Non-uniqueness for the Fokas-Olver-Rosenau-Qiao equation ⋮ Exact travelling wave solutions for the modified Novikov equation ⋮ An 𝑎𝑏-family of equations with peakon traveling waves ⋮ A view of the peakon world through the lens of approximation theory ⋮ The two-component Novikov-type systems with peaked solutions and \(H^1\)-conservation law ⋮ Weak solution of the Novikov equation and optimal control ⋮ Global analytic solutions and traveling wave solutions of the Cauchy problem for the Novikov equation ⋮ Optimal distributed controls of a class of nonlinear dispersive equations with cubic nonlinearity
This page was built for publication: The Periodic Cauchy Problem for Novikov's Equation