On the inverse scattering problem and the low regularity solutions for the Dullin-Gottwald-Holm equation

DOI10.1016/j.nonrwa.2009.01.031zbMath1186.35235OpenAlexW2077684757MaRDI QIDQ2655100

Guilong Gui, Xiaolian Ai

Publication date: 22 January 2010

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2009.01.031

zbMATH Keywords

bi-Hamiltonian structureinverse scattering problemDullin-Gottwald-Holm equationlow regularity solution

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) Inverse problems for PDEs (35R30) Existence, uniqueness, and regularity theory for incompressible inviscid fluids (76B03)

Related Items (12)

Classification of bounded travelling wave solutions for the Dullin-Gottwald-Holm equation ⋮ The Cauchy problem for a generalized Dullin–Gottwald–Holm equation in Besov spaces ⋮ Orbital stability of the sum of \(N\) peakons for the Dullin-Gottwald-Holm equation ⋮ On the solutions of the Dullin-Gottwald-Holm equation in Besov spaces ⋮ Various Exact Soliton Solutions and Bifurcations of a Generalized Dullin–Gottwald–Holm Equation with a Power Law Nonlinearity ⋮ The inverse scattering transform in the form of a Riemann-Hilbert problem for the Dullin-Gottwald-Holm equation ⋮ On an inverse scattering problem for a class of Dirac operators with spectral parameter in the boundary condition ⋮ EXACT TRAVELING WAVE SOLUTIONS AND BIFURCATIONS FOR THE DULLIN-GOTTWALD-HOLM EQUATION ⋮ Blow-up phenomena and global existence for the periodic two-component Dullin-Gottwald-Holm system ⋮ 1-soliton solution and conservation laws of the generalized Dullin-Gottwald-Holm equation ⋮ Existence and nonexistence of solutions for the generalized Camassa-Holm equation ⋮ Stability of singular waves for Dullin-Gottwald-Holm equation

Cites Work

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• Existence and uniqueness of low regularity solutions for the Dullin-Gottwald-Holm equation
• On the inverse scattering approach and action-angle variables for the Dullin-Gottwald-Holm equation
• Hamiltonian operators and algebraic structures related to them
• Well-posedness, blow up, and global existence for an integrable shallow water equation
• Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation
• Global existence and blow-up solutions for a nonlinear shallow water equation
• The limit behavior of the solutions to a class of nonlinear dispersive wave equations
• On the well-posedness problem and the scattering problem for the Dullin-Gottwald-Holm equation
• On the Inverse Scattering Approach to the Camassa-Holm Equation
• Local Well-Posedness and Orbital Stability of Solitary Wave Solutions for the Generalized Camassa–Holm Equation
• The nonlinear differential equation 𝑦”+𝑝(𝑥)𝑦+𝑐𝑦⁻³=0

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