Quantum nonlinear Schrödinger equation. II. Explicit solution
[For Part I see Ann. Inst. Henri Poincaré, Anal. Nonlinéaire 3, 285- 314 (1986; Zbl 0614.35086).] This is the second in a series of papers on the nonlinear Schrödinger equation (NLS) \[ \sqrt{-1}\psi_ t=-\psi_{xx}+2c\psi^+\phi^ 2, \] an evolution equation on the time-dependent ``annihilation operators'' \(\psi\) (x,t) on the Fock spaces \(\hat {\mathcal R}=\oplus^{\infty}_{N=0}{\mathcal H}_ N.\) Explicit formulas for the solution of the NLS in terms of ``collision expansions'' are obtained. The approach is based on the method of intertwining operators for the Hamiltonian \(\hat H\) on \(\hat {\mathcal H}\) which is formally given in terms of the creation and annihilation operators \(\psi^+\), \(\psi\) by \[ \hat H=\int^{\infty}_{-\infty}dx[-\psi^+\psi_{xx}+c\psi^+\psi^ 2]. \]
scientific article; zbMATH DE number 4132731
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