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Quantum nonlinear Schrödinger equation. II. Explicit solution. (English) Zbl 0692.35089
[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 $\hat H=\int^{\infty}_{-\infty}dx[-\psi^+\psi_{xx}+c\psi^+\psi^ 2].$
Reviewer: J.Weidmann

##### MSC:
 35Q99 Partial differential equations of mathematical physics and other areas of application 35K55 Nonlinear parabolic equations 35C05 Solutions to PDEs in closed form 81T99 Quantum field theory; related classical field theories
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##### References:
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