On Some Nonlinear Schrödinger Equations

  • H. Lange
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 75)


The equation which is studied in this note is the following nonlinear Schrodinger equation
$$ i\psi _t = \Delta \psi + \lambda v_q \left( \psi \right)^p \cdot\psi $$
$$ \psi = \psi \left( {x,t} \right),\,x \in \,R^3 ,\,t \in \,R,\,\,\lambda \, \in \,R,\,p,\,q \geqslant 1 $$
and (with r = |x|)
$$ v_q (\psi )\left( {x,t} \right) = (r^{ - 1} *\left| \psi \right|^{2q} )\left( {x,t} \right) = \int\limits_{R^3 } {\frac{{\left| {\psi \left( {y,t} \right)} \right|^{2q} }} {{\left| {x - y} \right|}}dy} {\text{ }} $$


Cauchy Problem Helium Atom Schrodinger Equation Nonlinear Coupling Nonlinear Eigenvalue Problem 
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Copyright information

© Plenum Press, New York 1981

Authors and Affiliations

  • H. Lange
    • 1
  1. 1.Mathematisches InstitutUniversität KölnWest Germany

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