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Integrability and soliton interaction of a resonant nonlinear Schrödinger equation via binary Bell polynomials. (English) Zbl 1270.37046
Summary: Under investigation in this paper is a resonant nonlinear Schrödinger equation for the response of a hypothetical resonance medium to an action of a quasimonochromatic wave or the propagation of one-dimensional long magnetoacoustic waves in a cold collisionless plasma subject to a transverse magnetic field. Binary Bell polynomials are employed to derive the bilinear form, Bäcklund transformation (BT) and Lax pair in the $$3\times 3$$ matrix form. Two sets of the binary Bell polynomials are considered. Infinite conservation laws are also constructed from the BT in the binary-Bell-polynomial form. Moreover, two-soliton solutions are obtained through the Hirota method. Finally, the regular, intermediate-state and resonant soliton interactions are analyzed under certain conditions.
##### MSC:
 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems 35C08 Soliton solutions 35Q55 NLS equations (nonlinear Schrödinger equations) 11B73 Bell and Stirling numbers 33C47 Other special orthogonal polynomials and functions
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