Integrable boundary conditions for higher-order nonlinear Schrödinger equation. (Chinese. English summary) Zbl 07801177
Summary: Based on Sklyanin’s formalism of integrable boundary, this paper studies integrable boundary conditions for the hierarchy of two-dimensional foucsing integrable nonlinear Schrödinger equations. We obtain, for even order nonlinear Schrödinger equations, a class of integrable boundary conditions; using the method of dressing the boundary, we construct soliton solutions of the equations on the half-line subject to integrable boundary conditions. As to half-line problems for odd order nonlinear Schrödinger equations, the formalism of integrable boundary only leads to a real reduction of the model: all the equations are reduced to real equations.
Keywords:
nonlinear Schrödinger equations; integrable hierarchy; integrable boundary conditions; half-line problems; soliton solutions; boundary conditions for NLSReferences:
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| [33] | Abstract Based on Sklyanin’s formalism of integrable boundary, this paper studies in-tegrable boundary conditions for the hierarchy of two-dimensional foucsing integrable non-linear Schrödinger equations. We obtain, for even order nonlinear Schrödinger equations, a class of integrable boundary conditions; using the method of dressing the boundary, we construct soliton solutions of the equations on the half-line subject to integrable boundary conditions. As to half-line problems for odd order nonlinear Schrödinger equations, the for-malism of integrable boundary only leads to a real reduction of the model: all the equations are reduced to real equations. Key words nonlinear Schrödinger equations; integrable hierarchy; integrable boundary conditions; half-line problems; soliton solutions; boundary conditions for NLS MR(2000) Subject Classification 35Q51; 35Q55 Chinese Library Classification 029 |
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