Non-uniform dependence on initial data for the Fornberg-Whitham equation in \(C^1(\mathbb{R})\)

KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Traveling wave solutions (35C07) Soliton solutions (35C08) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

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Well-posedness of the Fornberg-Whitham equation on the circle
Non-uniform dependence on initial data for the CH equation on the line.
Analyticity of periodic traveling free surface water waves with vorticity
Classification of travelling waves in the Fornberg-Whitham equation
Symplectic structures, their Bäcklund transformations and hereditary symmetries
Wave breaking for nonlinear nonlocal shallow water equations
On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves.
On the blow-up of solutions for the Fornberg-Whitham equation
Discontinuous traveling waves as weak solutions to the Fornberg-Whitham equation
Wave breaking analysis for the Fornberg-Whitham equation
Wave breaking of periodic solutions to the Fornberg-Whitham equation
Well-posedness and continuity properties of the Fornberg-Whitham equation in Besov spaces
Solution concepts, well-posedness, and wave breaking for the Fornberg-Whitham equation
The well-posedness, ill-posedness and non-uniform dependence on initial data for the Fornberg-Whitham equation in Besov spaces
Wave breaking for the Fornberg-Whitham equation
Non-uniform continuity in \(H^1\) of the solution map of the CH equation
New wave-breaking criteria for the Fornberg-Whitham equation
Wave breaking phenomena for the Fornberg-Whitham equation
Non-Uniform Dependence for the Periodic CH Equation
A numerical and theoretical study of certain nonlinear wave phenomena
Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle
An integrable shallow water equation with peaked solitons
Particle trajectories in solitary water waves
Variational methods and applications to water waves
Norm inflation and ill-posedness for the Fornberg-Whitham equation

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