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Asymptotics of convergence to a wave travelling from a saddle to a node

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Velocity asymptotics of the wave includes log t, challenging conventional representations.
An asymptotic solution is established for semilinear partial differential equations along two types.
The matching method is effectively applied to analyze the transition from a stable equilibrium.
The proposed method calculates universal asymptotics independently of initial conditions.

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Asymptotic analysis reveals velocity behavior of waves between stable and unstable equilibria, indicating new calculation methods.

L. A. Kalyakin (2025) studied this question.

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