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Darboux transformations of classical Boussinesq system and its new solutions. (English) Zbl 1115.35329

Summary: Two basic Darboux transformations of a spectral problem associated with a classical Boussinesq system are considered in this letter. They are used to generate new solutions of the classical Boussinesq system. An interesting solution of double-peak soliton has been found.

MSC:

35K15 Initial value problems for second-order parabolic equations
35A22 Transform methods (e.g., integral transforms) applied to PDEs
35Q35 PDEs in connection with fluid mechanics
35Q51 Soliton equations
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
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References:

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