Existence theorem establishes traveling wave solutions in generalized nonlinear reaction-diffusion equations, indicating wider applicability.
Existence theorem for the traveling wave solutions of the “generalized” nonlinear reaction-diffusion equation uₜ=(uᵐ)ₓₓ+f(u), is established for any $$m>1.$$ This form generalizes the classical linear form with $$m=1.$$ A critical value of the minimum wave speed c* is obtained as c*=2m√f(0), which extends the results obtained by Fisher, Kolmogorov, and others.
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Bougoffa et al. (2026) studied this question.
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