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General Rational Solutions and Soliton Solutions of the Nonlocal Resonant Nonlinear Schrodinger Equations. (arXiv:2305.16012v1 [nlin.SI])

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General rational solutions for the nonlocal resonant nonlinear Schrodinger
equations are derived by using the Hirota bilinear method and the KP hierarchy
reduction method. These rational solutions are presented in terms of
determinants in which the elements are algebraic expressions. A weaker
condition is given for KP reduction in the nonlocal case. The dynamics of
first-order solutions are investigated in details. As a special case, we
studied rantional solutions of the RNLS equation. Moreover, soliton solutions
of the RNLS equation are given by using the Backlund transformation and
nonlinear superposition formula.

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