The Cauchy problem for the Novikov equation
From MaRDI portal
Publication:5894524
DOI10.1088/0951-7715/25/2/449zbMath1232.35145OpenAlexW2064553589MaRDI QIDQ5894524
A. Alexandrou Himonas, Curtis Holliman
Publication date: 6 March 2012
Published in: Nonlinearity (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1088/0951-7715/25/2/449
KdV equations (Korteweg-de Vries equations) (35Q53) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Initial value problems for nonlinear first-order PDEs (35F25)
Related Items (only showing first 100 items - show all)
Wave breaking phenomenon for the generalized FORQ equation ⋮ An Inverse Spectral Problem Related to the Geng–Xue Two-Component Peakon Equation ⋮ A Cauchy-Kovalevsky Theorem for Nonlinear and Nonlocal Equations ⋮ The existence of the single peaked traveling waves to the -Novikov equation ⋮ The Cauchy problem for the Fokas-Olver-Rosenau-Qiao equation ⋮ The initial value problem for a Novikov system ⋮ Low regularity solutions, blowup, and global existence for a generalization of Camassa-Holm-type equation ⋮ Persistence properties and unique continuation for a generalized Camassa-Holm equation ⋮ Unnamed Item ⋮ Continuous properties of the data-to-solution map for a generalized μ-Camassa-Holm integrable equation ⋮ Construction of 2-Peakon Solutions and Ill-Posedness for the Novikov Equation ⋮ Non-uniform dependence on initial data for the Camassa-Holm equation in the critical Besov space ⋮ Ill-posedness for the Camassa-Holm and related equations in Besov spaces ⋮ Ill-posedness for a two-component Novikov system in Besov space ⋮ On the Cauchy problem of the two-component Novikov-type system with peaked solutions and H1-conservation law ⋮ Local and global analyticity for theμ-Novikov equation ⋮ On the Cauchy problem for the two-component Novikov system with peakons ⋮ On a generalized Camassa‐Holm type equation with ()‐degree nonlinearities ⋮ A note on the Cauchy problem for the periodic two-component Novikov system ⋮ The Cauchy problem for the Camassa-Holm-Novikov equation ⋮ Non-uniform continuity on initial data for the two-component b-family system in Besov space ⋮ Non-uniform continuous dependence and continuous dependence for the non-resistive MHD equations ⋮ Orbital stability of the trains of peaked solitary waves for the modified Camassa-Holm-Novikov equation ⋮ Estimates for \(\delta\)-periodic eigenvalues of two-component Novikov system ⋮ Blow-up analysis for the \(ab\)-family of equations ⋮ Continuity properties of the solution map for the four-component Novikov system with peakon solutions ⋮ Well-posedness and continuity properties of the Degasperis-Procesi equation in critical Besov space ⋮ On well-posedness of nonlocal evolution equations ⋮ Local well-posedness and blow-up criteria for a three-component Camassa–Holm type equation ⋮ Curvature blow-up and peakons for the Camassa-Holm type equation ⋮ Nonuniform dependence of the R‐b‐family system in Besov spaces ⋮ On the Cauchy problem for a four‐component Novikov system with peaked solutions ⋮ Local well-posedness and decay for some generalized shallow water equations ⋮ Global weak solutions to a nonlinear equation with fourth order nonlinearities ⋮ The Cauchy problem and multi-peakons for the mCH-Novikov-CH equation with quadratic and cubic nonlinearities ⋮ Bifurcation analysis and dynamics of abundant traveling waves of the modified Novikov equation ⋮ On a generalized Camassa–Holm equation with the flow generated by velocity and its gradient ⋮ Non-uniform dependence on initial data for the two-component Novikov system ⋮ Blow-up phenomena and the local well-posedness and ill-posedness of the generalized Camassa-Holm equation in critical Besov spaces ⋮ The Cauchy problem of a weakly dissipative shallow water equation ⋮ Nonuniform dependence and well-posedness for the generalized Camassa–Holm equation ⋮ On the Cauchy problem for a generalized Camassa-Holm equation ⋮ Global well-posedness and infinite propagation speed for the N − abc family of Camassa–Holm type equation with both dissipation and dispersion ⋮ Comparison Between the Exact Solutions of Three Distinct Shallow Water Equations Using the Painlevé Approach and Its Numerical Solutions ⋮ Hölder continuity of the solution map for the Novikov equation ⋮ Blow-up phenomena and peakons for the gFQXL/gCH-mCH equation ⋮ Stability in the energy space of the sum of N peakons for a modified Camassa-Holm equation with higher-order nonlinearity ⋮ The Cauchy problem for a generalized Camassa-Holm equation ⋮ Blow-up phenomena and local well-posedness for a generalized Camassa-Holm equation in the critical Besov space ⋮ Blow-up phenomena and local well-posedness for a generalized Camassa-Holm equation in the critical Besov space ⋮ On the Cauchy problem for the generalized Camassa-Holm equation ⋮ On the Cauchy problem of generalized Fokas–Olver–Resenau–Qiao equation ⋮ Nonuniform dependence and persistence properties for a two-component Novikov system ⋮ Unnamed Item ⋮ Non-uniform continuous dependence on initial data of solutions to the Euler-Poincaré system ⋮ The Cauchy problem for a family of generalized Camassa–Holm equations ⋮ An 𝑎𝑏-family of equations with peakon traveling waves ⋮ The existence of global weak solutions for a generalized Camassa–Holm equation ⋮ The well-posedness, blow-up, and traveling waves for a two-component Fornberg–Whitham system ⋮ Global existence and long time behavior of the generalized Camassa–Holm equation with k + 1 degree nonlinearities ⋮ A direct algorithm of one-dimensional optimal system for the group invariant solutions ⋮ The Cauchy problem for a generalized Camassa–Holm equation with the velocity potential ⋮ The global weak solutions to the Cauchy problem of the generalized Novikov equation ⋮ Periodic peakons to a generalized μ-Camassa–Holm–Novikov equation ⋮ Lower order regularity for the generalized Camassa–Holm equation ⋮ A note on the solution map for the periodic Camassa–Holm equation ⋮ Well-posedness of the Fornberg-Whitham equation on the circle ⋮ Sharp ill-posedness for the generalized Camassa-Holm equation in Besov spaces ⋮ The stability of solutions for the Fornberg-Whitham equation in \(L^1(\mathbb{R})\) space ⋮ On the Cauchy problem and peakons of a two-component Novikov system ⋮ Persistence properties for the Fokas-Olver-Rosenau-Qiao equation in weighted \(L^{p}\) spaces ⋮ Some properties of solutions to the Camassa-Holm-type equation with higher-order nonlinearities ⋮ Liouville correspondences between integrable hierarchies ⋮ The periodic Cauchy problem for a combined CH-mCH integrable equation ⋮ Instability and nonuniqueness for the \(b\)-Novikov equation ⋮ The Cauchy problem for a generalized two-component short pulse system with high-order nonlinearities ⋮ The Cauchy problem for a 4-parameter family of equations with peakon traveling waves ⋮ A Riemann-Hilbert approach for the Novikov equation ⋮ Non-uniform continuous dependence on initial data for a two-component Novikov system in Besov space ⋮ Well-posedness and blow-up phenomena for a generalized Camassa-Holm 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 ⋮ Remarks on the well-posedness of Camassa-Holm type equations in Besov spaces ⋮ Nonuniqueness for the \(ab\)-family of equations with peakon travelling waves on the circle ⋮ On an integrable Camassa-Holm type equation with cubic nonlinearity ⋮ Well-posedness and blow-up phenomena for an integrable three-component Camassa-Holm system ⋮ Stability of peakons for an integrable modified Camassa-Holm equation with cubic nonlinearity ⋮ On the Cauchy problem for a class of cubic quasilinear shallow-water equations ⋮ Periodic wave solutions and their limit forms of the modified Novikov equation ⋮ The investigation of local weak solutions for a generalized Novikov equation ⋮ On the curvature blow-up phenomena for the Fokas-Qiao-Xia-Li 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 ⋮ Qualitative analysis for the new shallow-water model with cubic nonlinearity ⋮ Stability of peakons for the Novikov equation ⋮ Wave-breaking phenomena for a weakly dissipative shallow water equation ⋮ A Nash-Moser approach for the Euler-Arnold equations ⋮ Global existence and propagation speed for a generalized Camassa-Holm model with both dissipation and dispersion ⋮ Well-posedness and global existence for a generalized Degasperis-Procesi equation ⋮ Autonomous Ovsyannikov theorem and applications to nonlocal evolution equations and systems
This page was built for publication: The Cauchy problem for the Novikov equation