On Blow-Up Solutions for the Fourth-Order Nonlinear Schrödinger Equation with Mixed Dispersions

Abstract

In this paper, we consider blow-up solutions for the fourth-order nonlinear Schrödinger equation with mixed dispersions. We study the dynamical properties of blow-up solutions for this equation, including the H˙γc-concentration and limiting profiles, which extend and improve the existing results in the literature.

Keywords

• fourth-order nonlinear Schrödinger equation
• blow-up behavior
• minimizers
• H ˙ γ c -critical%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <named-content content-type="inline-formula"><inline-formula><mml:math id="mm99991"> <mml:semantics> <mml:msup> <mml:mover accent="true"> <mml:mi>H</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:msub> <mml:mi>γ</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:msup> </mml:semantics> </mml:math> </inline-formula></named-content>-critical