We consider the Cauchy problem for the higher-order nonlinear Schrödinger equation (Formula presented.), where k, p∈ N, k≥ 2 , λ∈ C. We prove local existence of solutions for the case of singular initial data u0(x) including the Dirac delta function.
- Higher-order nonlinear Schrödinger equation
- Local existence
- Weighted Sobolev space