Self-similar blow-up solutions in the generalised Korteweg-de Vries equation: spectral analysis, normal form and asymptotics

KdV equations (Korteweg-de Vries equations) (35Q53) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Eigenvalue problems for linear operators (47A75) Normal forms for dynamical systems (37G05) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Bifurcations in context of PDEs (35B32) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10) Blow-up in context of PDEs (35B44) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08) Symmetries, invariants, etc. in context of PDEs (35B06) Self-similar solutions to PDEs (35C06) Finite volume methods for boundary value problems involving PDEs (65N08)

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