k-contact geometry supplies explicit Hamiltonian descriptions for multiple dissipative PDEs including damped Klein-Gordon, Allen-Cahn, Fisher-KPP, and complex Ginzburg-Landau equations.
The Burgers-FKPP advection-reaction- diffusion equation with cut-off
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For the generalized Burgers-Fisher-KPP equation, Heaviside-type initial data converge to traveling waves at critical velocities, with a convection coefficient threshold k* separating vanishing and spreading regimes.
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A Guide to Applications of $k$-Contact Geometry in Dissipative Field Equations
k-contact geometry supplies explicit Hamiltonian descriptions for multiple dissipative PDEs including damped Klein-Gordon, Allen-Cahn, Fisher-KPP, and complex Ginzburg-Landau equations.
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Large time behavior and transition from vanishing to spreading regimes for the generalized Burgers-Fisher-KPP equation
For the generalized Burgers-Fisher-KPP equation, Heaviside-type initial data converge to traveling waves at critical velocities, with a convection coefficient threshold k* separating vanishing and spreading regimes.