Ill-posedness estimation of the derivative schrödinger equation with a fourth-order power nonlinear term in H s

Key Points

• The research aims to explore the stability and soliton solutions of a nonlinear Schrödinger equation with fourth-order terms.
• Constructed a family of soliton solutions for the derivative nonlinear Schrödinger equation.
• Proved a strong instability phenomenon in Sobolev spaces (H^s).
• Used refined Fourier integral estimates to analyze instability thresholds.
• Identified (1/4) as the upper threshold for the instability index in H^s.
• Demonstrated the existence of strong instability in the associated flow.
• Provided insights into the implications of nonlinearity on stability within the equation.