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Wronskian solutions to integrable equations. (English) Zbl 1184.37057
Summary: Wronskian determinants are used to construct exact solution to integrable equations. The crucial steps are to apply Hirota’s bilinear forms and explore linear conditions to guarantee the Plücker relations. Upon solving the linear conditions, the resulting Wronskian formulations bring solution formulas, which can yield solitons, negatons, positions and complexitons. The solution process is illustrated by the Korteweg-de Vries equation and applied to the Boussinesq equation.

MSC:
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q51 Soliton equations
35Q53 KdV equations (Korteweg-de Vries equations)
35Q55 NLS equations (nonlinear Schrödinger equations)
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