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Hamiltonian Theory for the DNLS Equation with a Squared Spectral Parameter

Hamiltonian Theory for the DNLS Equation with a Squared Spectral Parameter
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摘要 With a special gauge transformation,the Lax pair of the derivative nonlinear Shcrdinger (DNLS) equation turns to depend on the squared parameter λ = k2instead of the usual spec-tral parameter k. By introducing a new direct product of Jost solu-tions,the complete Hamiltonian theory of the DNLS equation is constructed on the basis of the squared spectral parameter,which shows that the integrability completeness is still preserved. This result will be beneficial to the further study of the DNLS equation,such as the direct perturbation method. With a special gauge transformation,the Lax pair of the derivative nonlinear Shcrdinger (DNLS) equation turns to depend on the squared parameter λ = k2instead of the usual spec-tral parameter k. By introducing a new direct product of Jost solu-tions,the complete Hamiltonian theory of the DNLS equation is constructed on the basis of the squared spectral parameter,which shows that the integrability completeness is still preserved. This result will be beneficial to the further study of the DNLS equation,such as the direct perturbation method.
出处 《Wuhan University Journal of Natural Sciences》 CAS 2010年第4期315-319,共5页 武汉大学学报(自然科学英文版)
基金 Supported by the National Natural Science Foundation of China (10705022)
关键词 DNLS equation Hamiltonian theory squared spectral parameter inverse scattering transform PERTURBATION DNLS equation Hamiltonian theory squared spectral parameter inverse scattering transform perturbation
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