|Title of the article||
SOLITON SOLUTIONS OF NONLINEAR SCHRÖDINGER-TYPE EQUATIONS AND FUNCTIONAL SUBSTITUTIONS
Zhuravlev Viktor Mikhaylovich, Doctor of physical and mathematical sciences, professor, sub-department of theoretical physics, Ulyanovsk State University (42 Lva Tolstogo street, Ulyanovsk, Russia), email@example.com
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Background. The main goal of the paper is to establish the relationship between the inverse problem method (IPM) and the method of functional substitutions (MFS) in the theory of integrable nonlinear partial differential equations. The inverse problem method is used to construct solutions of equations admitting multi-soliton solutions, and the method of functional substitutions to equations, which are often called Burgers type equations. In this paper, it is demonstrated that modifying the MFS by introducing additional closing conditions into the procedure makes it possible to derive Burgers-type equations for equations that coincide with equations integrable by means of MOS. In this paper we study only equations of the type of the nonlinear Schrödinger equation (NLS), and Ginzburg – Landau equations.
exactly integrable nonlinear equations, generalized functional substitutions, exact solutions of generalized nonlinear Schrödinger and Ginzburg – Landau equations
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