Spectral Stability of Nonlinear Waves in KdV‐Type Evolution Equations

This chapter focuses on the spectral stability of nonlinear waves in Korteweg‐de Vries (KdV) type evolution equations. The relevant eigenvalue problem is defined by the composition of an unbounded self‐adjoint operator with a finite number of negative eigenvalues and an unbounded non‐invertible operator ∂x. The instability index theorem is proven under a generic assumption on the self‐adjoint operator both in the case of solitary waves and …